Events

May 10 - May 4, 2014

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  Response Surface in low-rank Tensor Train Format for Uncertainty Quantification by Dr. Alexander Litvinenko

  Alexander Litvinenko, Senior Research Scientist, Stochastic Numerics Research Group

  May 5, 16:00 - 17:00

  B9 H2 SHAXC 2 Workshop

  Alexander Litvinenko joined the Stochastic Numerics Group and Strategic Initiative in Uncertainty Quantification at KAUST in 2013. He specializes in efficient numerical methods for stochastic PDEs, uncertainty quantification, and multi-linear algebra. He is involved in Bayesian update methods for solving inverse problems, with the goal of reducing the complexity both the stochastic forward problem as well as the Bayesian update by a low-rank (sparse) tensor data approximation.
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  Random Flights By Prof. Enzo Orsingher

  Prof. Enzo Orsingher, Sapienza University of Rome, Italy

  May 4, 14:00 - 15:00

  B1 R4214

  In R1 we discuss the telegraph process and give the main distributional results. We consider also the case of the asymmetric telegraph process and use relativistic transformations for its probabilistic analysis. Random motions in the plane with infinite and with a finite number of possible directions of motion are discussed.

May 3 - Apr 27, 2014

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  Basic Principles of Mixed Virtual Element Methods By Prof. L. Donatella Marini (Universita di Pavia, Italy)

  Prof. L. Donatella Marini

  Apr 29, 15:00 - 16:00

  B1 R4214

  We present, in the simplest possible way, the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields. As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear.
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  Virtual Element Methods for linear elliptic PDEs

  Prof. Franco Brezzi, Istituto Universitario di Studi Superiori - IUSS, Italy

  Apr 28, 15:00 - 16:00

  B9 H1 R2322

  The seminar will present the basic structure and the fundamental ideas behind the Virtual Element Methods, taking, for simplicity, the Laplace operator as toy example. The main features of the method will be sketched, together with the guidelines for its implementation and the essential mathematical instruments to be used in the analysis.

Apr 26 - Apr 20, 2014

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  Hierarchical matrix introduction course by Dr. Alexander Litvinenko and Dr. Rio Yokota

  Alexander Litvinenko, Senior Research Scientist, Stochastic Numerics Research Group

  Apr 22, 16:00 - Apr 23, 18:30

  KAUST Library

  Alexander Litvinenko joined the Stochastic Numerics Group and Strategic Initiative in Uncertainty Quantification at KAUST in 2013. He specializes in efficient numerical methods for stochastic PDEs, uncertainty quantification, and multi-linear algebra. He is involved in Bayesian update methods for solving inverse problems, with the goal of reducing the complexity both the stochastic forward problem as well as the Bayesian update by a low-rank (sparse) tensor data approximation.
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  Bayesian inference as optimal transportation By Prof. Youssef Marzouk Massachusetts Institute of Technology, USA

  Prof. Youssef Marzouk, Massachusetts Institute of Technology, USA

  Apr 22, 14:00 - 15:00

  B1 R4214

  bayesian inference sequential Monte Carlo

  Bayesian inference provides a natural framework for quantifying uncertainty in parameter estimates and model predictions, for combining heterogeneous sources of information, and for conditioning sequential predictions on data. Posterior simulation in Bayesian inference often proceeds via Markov chain Monte Carlo (MCMC) or sequential Monte Carlo (SMC), but the associated computational expense and convergence issues can present significant bottlenecks in large-scale or dynamically complex problems.
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  On the subsolution approach to efficient importance sampling By Prof. Boualem Djehiche (KTH, Stockholm, Sweden)

  Professor of mathematical statistics, KTH, Sweden

  Apr 21, 15:00 - 16:00

  B1 R4214

  The widely used Monte Carlo simulation technique where all the particles are independent and statistically identical and their weights are constant is by no means universally applicable. The reason is that particles may wander off to irrelevant parts of the state space, leaving only a small fraction of relevant particles that contribute to the computational task at hand. Therefore it may require a huge number of particles to obtain a desired precision, resulting in a computational cost that is too high for all practical purposes.

Apr 12 - Apr 6, 2014

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  Scalable hierarchical algorithms for PDEs and UQ By Dr. Alexander Litvinenko and Dr. Rio Yokota

  Alexander Litvinenko, Senior Research Scientist, Stochastic Numerics Research Group

  Apr 10, 12:00 - 13:00

  B9 H1

  Hierarchy is a key ingredient for achieving optimal arithmetic complexity and scalable communication complexity in algorithms. Fast Multipole Methods (FMM) and H-matrices share many common features that arise from their hierarchical nature. In this talk, Rio Yokota will illustrate the common features between FMM and H-matrices and how these features are favorable on computer architectures of the next generation.

Mar 29 - Mar 23, 2014

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  SDEs with irregular coefficients By Prof. Arturo Kohatsu (Ritsumeikan University, Japan)

  Prof. Arturo Kohatsu, Ritsumeikan University, Japan

  Mar 27, 14:00 - 15:00

  B1 R4214

  stochastic differential equations

  In this talk we will give some results regarding the existence and regularity of densities for stochastic differential equations (sde's) with irregular coefficients starting with Holder coefficients and then bounded and measurable. If time allows we will also discuss issues related to the simulation schemes for such sde's.
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  MCMC Sampling of Posterior Probability Distributions over Fields by Dr. Kody Law

  Kody J. H. Law, Senior Research Scientist, Stochastic Numerics Research Group

  Mar 25, 11:00 - 12:00

  B9 R4222

  In many problems in science and engineering, one would like to perform inference on parametric fields, of space and/or time, in order to reduce uncertainties and improve predictive capabilities, for example, the computation of quantities of interest such as outputs of the model or various expectations thereof. Examples of such fields include the initial condition of fluid dynamical equations in the context of numerical weather prediction and oceanography, the permeability and porosity of multiphase subsurface flow in the context of oil exploration, or the forcing of a stochastic dynamical system in the context of molecular dynamics.

Mar 15 - Mar 9, 2014

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  Optimal Control and User Incentives in Cyber-Physical Systems by Dr. Hamidou Tembine

  Hamidou Tembine, Senior Research Scientist, Stochastic Numerics Research Group

  Mar 9, 11:00 - 12:00

  B9 R4222

  In this talk, we focus on two sample applications: traffic networks and smart energy systems. We will explain how optimal control tools and user incentive designs can be used to better manage traffic congestion and address demand response in medium and large-scale systems.

Mar 8 - Mar 2, 2014

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  An a posteriori error estimate for Symplectic Euler approximation of optimal control problems By Prof. Mattias Sandberg

  Prof. Mattias Sandberg Associate Professor, KTH Royal Institute of Technology, Sweden

  Mar 6, 15:00 - 16:00

  B1 R4214

  The analysis and performance of numerical computations for optimal control problems is complicated by the fact that they are ill-posed. It is for example often the case that optimal solutionsdepend discontinuously on data. Moreover, the optimal control, if it exists, may be a highly non-regular function, with many points of discontinuity etc. On the other hand optimal control problems are well-posed in the sense that the associated value function is well-behaved, with such properties as continuous dependence on data.
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  Richardson extrapolation and finite difference schemes for SPDEs By Dr. Eric Joseph Hall

  Dr. Eric Joseph Hall, Postdoctoral Fellow, KTH Royal Institute of Technology, Sweden

  Mar 5, 14:30 - 15:30

  B1 R4214

  Stochastic partial differential equations (SPDEs) are used in many areas of applied science and engineering. Examples of systems that are modeled by SPDEs arise in applications as diverse as satellite guidance, tumor detection and financial markets. In many instances analytic solutions to these equations are unavailable and approximations with a high order of accuracy are difficult to obtain.
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  Mathematical, Computational and Theoretical Epidemiology: Challenges and Opportunities

  By Prof. Carlos Castillo-Chavez, Regents Professor and Joaquin Bustoz Jr. Professor of Mathematical Biology at Arizona State University

  Mar 3, 15:00 - 16:00

  B9 H1

  The marriage of mathematics and epidemics has a long and distinguished history with a plethora of successes that go back to the work of Daniel Bernoulli (1700 – 1782) and Nobel Laureate and physician Sir Ronald Ross (1911) and associates. These individuals, mostly physicians, created the field of mathematical epidemiology in their efforts to meet their commitment to diminish health disparities, the consequences of poverty and the lack of access to health services.

Mar 1 - Feb 23, 2014

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  Exact Sampling and Inference for Non-Linear Stochastic Differential Equations. Short course By Prof. Alexandros Beskos (Associate Professor at NUS, Singapore)

  Prof. Alexandros Beskos, Associate Professor at NUS, Singapore

  Feb 27, 15:00 - 16:30

  B1 R4214

  Exact Sampling and Inference for Non-Linear Stochastic Differential Equations. I will present a surprisingly simple algorithm we developed some years ago for the exact simulation of non-linear diffusion processes. Exact sampling of such processes was considered impossible for such models. The presence of stochasticity allows for developing a rejection sampling algorithm by proposing candidate Brownian paths; the accept/reject rule then involves events of an appropriate Poisson process. We have thus termed the method the Weiner-Poisson factorization of a non-linear SDE. The developed sampling method provides also a natural approach for carrying out maximum-likelihood-based inference for unknown parameters of the SDE.
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  Sequential Monte Carlo Samplers for Applications in High Dimensions Short course By Prof. Alexandros Beskos (Associate Professor at NUS, Singapore)

  Prof. Alexandros Beskos

  Feb 26, 09:00 - Sep 18, 10:30

  B1 R4214

  Sequential Monte Carlo (SMC) methods are nowadays routinely applied in a variety of complex applications: hidden Markov models, dynamical systems, target tracking, control problems, just to name a few. Whereas SMC methods have been greatly refined in the last decades and are now much better understood, they are still known to suffer from the curse of dimensionality: algorithms can sometimes break down exponentially fast with the dimension of the state space. As a consequence, practitioners in high-dimensional Data Assimilation applications in atmospheric sciences, oceanography and elsewhere will typically use 3D-Var or Kalman-filter-type approximations that will provide biased estimates in the presence of non-linear model dynamics.
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  Mean Field Games and Mean Field Type Control By Prof. Alain Bensoussan (Ashbel Smith Professor and Director of the International Center for Decision and Risk Analysis (ICDRiA), University of Texas at Dallas, USA)

  Prof. Alain Bensoussan, Ashbel Smith Professor and Director of the International Center for Decision and Risk Analysis (ICDRiA), University of Texas at Dallas, USA

  Feb 25, 14:00 - 15:00

  B1 R4214

  This is a joint work with Professor Jens Frehse and Professor Phillip Yam. We give a unified presentation of two research domains which have been very popular in the recent years, but considered independently. We provide a Dynamic Programming as well as a Stochastic Maximum Principle approach. We discuss many extensions and the issue of time consistency. Extended slides will be provided.

Feb 22 - Feb 16, 2014

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  Data Assimilation - Part 2

  Kody J. H. Law, Senior Research Scientist, Stochastic Numerics Research Group

  Feb 20, 15:00 - 17:30

  B3 R5520

  data assimilation

  Please register in advance at: Registration See please the program here: Schedule​ See lecture notes here: Notes​ See Melanie Ades notes - Part I: Slides See MATLAB code here: Code See Mealine Ades notes - Part II: Slides ​See Kody Law notes here: Slides​
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  Data Assimilation - Part 1

  Kody J. H. Law, Senior Research Scientist, Stochastic Numerics Research Group

  Feb 17, 09:00 - 11:15

  B3 R5520

  data assimilation

  Please register in advance at: Registration See please the program here: Schedule​ See lecture notes here: Notes​ See Melanie Ades notes - Part I: Slides See MATLAB code here: Code See Mealine Ades notes - Part II: Slides ​See Kody Law notes here: Slides​

Feb 15 - Feb 9, 2014

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  Game Theory Meets Computer Science and Engineering by Dr. Hamidou Tembine

  Hamidou Tembine, Senior Research Scientist, Stochastic Numerics Research Group

  Feb 11, 11:00 - 12:00

  B9 R4222

  Game Theory has been a staple of economics research since 1950, when John Nash who is the subject of the movie A Beautiful Mind, published the seminal paper that would win him the Nobel Prize in economics. As game theory has matured, it’s become even more central to the field of economics and social sciences.
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  Uncertainty quantification in Discrete Fracture Network models By Prof. Claudio Canuto (Dipartimento di Scienze Matematiche, Politecnico di Torino, Italy)

  Prof. Claudio Canuto, Polytechnic of Turin, Italy

  Feb 10, 15:00 - 16:00

  B1 R4214

  discrete fracture network

  Discrete Fracture Network (DFN) models are widely used in the simulation of subsurface flows; they describe a geological reservoir as a system of many intersecting planar polygons representing the underground network of fractures. Among the different approaches to DFN simulations, recently (Berrone et al, 2013) a numerical model has been formulated as a PDE-constrained optimization problem, in which neither fracture/fracture nor fracture/trace mesh conformity is required.

Feb 8 - Feb 2, 2014

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  Overview of numerical methods for quantification of uncertainties by Dr. Alexander Litvinenko

  Alexander Litvinenko, Senior Research Scientist, Stochastic Numerics Research Group

  Feb 4, 11:00 - 12:00

  B9 R4222

  In this talk, I will explain what is uncertainty quantification and how to model uncertainties via random variables/random fields. I will give several examples of stochastic partial differential equations with uncertain coefficients, uncertain computations domain, uncertain right-hand side, or boundary conditions.
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  WEP 2014 - Distributed Strategic Learning by Dr. Hamidou Tembine

  Hamidou Tembine, Senior Research Scientist, Stochastic Numerics Research Group

  Feb 2, 11:00 - 12:00

  B9 R4222

  This course will introduce the audience to some of the essential ingredients of learning in games under uncertainty (random matrix games), particularly reinforcement learning, cost-of-learning, Q-learning, mean-field learning, combined learning, heterogeneous learning and hybrid learning.

Jan 11 - Jan 5, 2014

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  Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2014)

  Raul Tempone, Professor, Applied Mathematics and Computational Science

  Jan 6, 09:00 - Jan 10, 17:00

  B4 B5 A0215

  uncertainty quantification algorithms

  ​SRI UQ Annual Meeting 6-10 January 2014 See please the program here: schedule Technical presentations slide: here Full Book of Abstracts: here Full Book of Abstracts with Posters: here​ ​(40 MB)

Nov 30 - Nov 24, 2013

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  Hybrid Adaptive Multilevel Monte Carlo Algorithm for Non-Smooth Observables of It ô Stochastic Differential Equations by Nadhir Ben Rached

  Nadhir Ben Rached, Ph.D., Applied Mathematics and Computational Science

  Nov 27, 10:30 - 12:00

  B1 R4214

  The Monte Carlo forward Euler method with uniform time stepping is the standard technique to compute an approximation of the expected payoff of a solution of an Itô SDE. For a given accuracy requirement TOL, the complexity of this technique for well-behaved problems, that is the amount of computational work to solve the problem, is O(TOL-3).
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  Discontinuous Galerkin approximation to the Vlasov-Poisson system By Dr. Blanca Ayuso de Dios (Centre de Recerca Matematica at Barcelona) ​

  Dr. Blanca Ayuso de Dios, Centre de Recerca Matematica at Barcelona

  Nov 25, 15:00 - 16:00

  B1 R4214

  Partial Differential Equations

  One of the simplest model problems in the kinetic theory of plasma--physics is the Vlasov-Poisson system with periodic boundary conditions. Such system describes the evolution of a plasma of charged particles (electrons and ions) under the effects of the transport and self-consistent electric field. In this talk, we present a family of discontinuous Galerkin (DG) methods for the approximation of the Vlasov-Poisson system.

Nov 2 - Oct 27, 2013

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  A Sample from the Stochastic Numerics Group by Prof. Raul Tempone

  Raul Tempone, Professor, Applied Mathematics and Computational Science

  Oct 31, 12:00 - 13:00

  B9 L2 R2322 H1

  I will provide a quick glance into the research of my group, giving particular emphasis on the activities of my KAUST students. This will hopefully give a connection between our research and our educational activities.

Oct 5 - Sep 29, 2013

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  An Introduction to Stochastic Control Theory By Prof. Boualem Djehiche (KTH Royal Institute of Technology, Stockholm, Sweden)

  Prof. Boualem Djehiche, KTH Royal Institute of Technology, Stockholm, Sweden

  Oct 1, 15:30 - Oct 6, 17:00

  B1 R4214

  The course treats completely observed control problems with a state equation of Itô type and with a performance function which is the expected value of a functional of the controlled process. As is well known, Bellman's dynamic programming leading to the celebrated Hamilton-Jacobi-Bellman equation and Pontryagin's maximum principle are the most commonly used approaches to solving the control problem.

Apr 27 - Apr 21, 2013

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  SRI UQ Annual Workshop 2013

  Raul Tempone, Professor, Applied Mathematics and Computational Science

  Apr 26, 09:00 - Apr 30, 17:00

  Auditorium L0 Between B4 and B5

  uncertainty quantification

  Apr 26 2013 9:00 AM - Apr 30 2013 5:00 PM SRI UQ Annual Meeting 26-30 April 2013 Schedule_2013 To view the WORKSHOP report please click on this link: Report

Mar 30 - Mar 24, 2013

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  Bayesian Analysis of Stochastic Process Models (AMCS 390) By Prof. Fabrizio Ruggeri (Italian National Research Council, Milano, Italy)

  Prof. Fabrizio Ruggeri, Italian National Research Council, Milano, Italy

  Mar 25, 10:30 - Apr 24, 12:00

  B9 R2132

  The student will be introduced to Bayesian modeling in selected, but relevant, stochastic processes and their applications: Markov chains, Poisson processes, reliability and queues. The use of real examples will be helpful in understanding why and how perform a Bayesian analysis. Students will be asked to analyze real data, from the elicitation of priors and modeling to (numerical) computation of estimates and forecasts and interpretation of findings.
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  Ensemble Kalman Methods For Inverse Problems By Prof. Andrew Stuart (Warwick University, United Kingdom)

  Prof. Andrew Stuart, Warwick University, United Kingdom

  Mar 24, 15:00 - 16:00

  B1 R4214

  Many problems in the physical sciences require the determination of an unknown field from a finite set of indirect measurements. Examples include oceanography, oil recovery, water resource management and weather forecasting. This may be formulated as a least squares problem to match the model output to the data. I will demonstrate that ideas from the Ensemble Kalman Filter can be adapted to solve such problems: by running multiple interacting copies of the model, and exposing their output to the (suitably randomized) data, a derivative-free minimization tool is constructed.

Mar 16 - Mar 10, 2013

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  Uncertainty Quantification in Molecular Dynamics By Dr. Francesco Rizzi (John Hopkins University, USA)

  Dr. Francesco Rizzi, John Hopkins University, USA

  Mar 13, 15:00 - 16:00

  B1 R3119

  uncertainty quantification

  Molecular dynamics (MD) is widely employed in both industrial and academic environments, playing a key role in the study of a large variety of systems, ranging fromliquids to solids, as well as biomolecules, such as proteins and nucleic acids (DNA, RNA). MD simulations provide a suitable and convenient method to explore dynamical properties of a system at the atomic level which, in general, aresignificantly difficult and expensive to investigate in experimental settings.

Mar 9 - Mar 3, 2013

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  Parametric Problems, Stochastic, and Identification By Prof. Hermann Matthies (ISCTUB, Germany)

  Prof. Hermann Matthies, Institute of Scientific Computing TU Braunschweig, Geramany

  Mar 6, 15:00 - 16:00

  B1 R4102

  Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily incorporating new information, e. g. through a measurement, by connecting it to Bayes's theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a description has two constituents, the measurable function and the measure.

Feb 16 - Feb 10, 2013

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  Accurate Filtering With 3DVAR For Dissipative Systems By Dr. Kody Law (University of Warwick, United Kingdom)

  Dr. Kody Law, Postdoctoral Research Fellow, University of Warwick, United Kingdom

  Feb 11, 15:00 - 16:00

  B1 R4214

  Unstable dynamical systems can be stabilized, and hence the solution recovered from noisy data, provided two conditions hold. First, observe enough of the system: the unstable modes. Second, weight the observed data sufficiently over the model. In this talk I will illustrate this for the 3DVAR filter applied to three dissipative dynamical systems of increasing dimension: the Lorenz 1963 model, the Lorenz 1996 model, and the 2D Navier-Stokes equation.

Dec 8 - Dec 2, 2012

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  PDE with Random Coefficients As A Problem in High-Dimensional Numerical Integration By Prof. Ian H. Sloan (University of New South Wales, Australia)

  Prof. Ian H. Sloan, University of New South Wales, Australia

  Dec 2, 15:00

  B1 R4214

  Partial Differential Equations

  This talk is concerned with the use of quasi-Monte Carlo methods combined with finite-element methods to handle an elliptic PDE with a random field as a coefficient. A number of groups have considered such problems (under headings such as polynomial chaos, stochastic Galerkin and stochastic collocation) by reformulating them as deterministic problems in a high dimensional parameter space, where the dimensionality comes from the number of random variables needed to characterize the random field.

Nov 17 - Nov 11, 2012

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  On Generalized Fiducial Inference By Prof. Jan Hannig (Univ. of Carolina at Chapel Hill, USA)

  Prof. Jan Hannig University of North Carolina at Chapel Hill

  Nov 13, 16:30 - 17:30

  B1 R4214

  R. A. Fisher's fiducial inference has been the subject of many discussions and controversies ever since he introduced the idea during the 1930's. The idea experienced a bumpy ride, to say the least, during its early years and one can safely say that it eventually fell into disfavor among mainstream statisticians. However, it appears to have made a resurgence recently under various names and modifications.
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  Rethinking Uncertainty Quantification By Prof. Edward Boone

  Prof. Edward Boone, Associate Professor, Department of Statistical Sciences and Operations Research

  Nov 12, 15:00 - 16:00

  B1 R4214

  Model Validation is often a difficult task with many different objectives and their associated metrics. Many times these metrics can address a single issue such as model fit, predictive performance, uncertainty quantification, etc. One quantity of interest is the amount of uncertainty associated with model misspecification. In this talk we present a bootstrap based method for uncertainty quantification under model misspecification.
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  Bayesian Estimation Of Thermal Conductivity in Polymethyl Methacrylate By Prof. Fabrizio Ruggeri (Italian National Research Council, Milano, Italy)

  Prof. Fabrizio Ruggeri, Italian National Research Council, Milano, Italy

  Nov 11, 15:00 - 16:00

  B1 R4214

  Bayesian approach is developed for estimating the thermal conductivity of a homogeneous material from the temperature evolution acquired in few internal points. Temperature evolution is described by the classical one-dimensional heat equation, in which the thermal conductivity is one of the coefficients.

Nov 10 - Nov 4, 2012

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  Approximation of Stochastic PDE’s Involving White Noises By Prof. Hassan Manouzi (Laval University, Quebec, Canada)

  Prof. Hassan Manouzi, Applied Mathematics, Laval University, Quebec, Canada

  Nov 5, 15:00 - 16:00

  B1 R2418

  Stochastic partial differential equations (SPDEs) play fundamental and important roles in many problems and their numerical simulations become useful and important in practical applications. The mathematical treatment of SPDEs represents however a greater challenge in comparison to deterministic partial differential equations.

Oct 6 - Sep 30, 2012

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  Gaussian Beam Approximations of High Frequency By Prof. Olof Runborg (KTH, Sweden)

  Prof. Olof Runborg, Royal Institute of Technology (KTH), Stockholm, Sweden

  Oct 2, 15:00 - 16:00

  B1 R4214

  Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a curve through the domain. Superpositions of Gaussian beams provide a tool to generate more general high frequency solutions. In contrast to the standard geometrical optics, the Gaussian beam approximation does not break down at caustics.

Sep 29 - Sep 23, 2012

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  Covariance Eigenproblems and their Numerical Treatment By Prof. Oliver Ernst (Technical University Bergakademie Freiberg, Germany) ​

  Prof. Oliver Ernst, Technical University Bergakademie Freiberg, Germany

  Sep 26, 15:00 - 16:00

  B1 R4214

  One of the most versatile parametrizations of stochastic processes or random fields for large-scale computations is provided by the Karhunen-Loève expansion. Its computational realization requires (at least the partial) solution of an eigenvalue problem for a covariance operator.

Sep 22 - Sep 16, 2012

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  Sharp Complexity Bounds For Computing Quadrature Formulas for Marginal Distribution of SDEs By Prof. Thomas Mueller (University of Passau, Germany)

  Prof. Thomas Mueller, University of Passau, Germany

  Sep 17, 15:00 - 16:00

  B1 R4214

  We consider the problem of approximating the marginal distribution of the solution of a stochastic differential equation (SDE) by probability measures with finite support, i.e., by quadrature formulas with positive weights summing up to one. We study deterministic algorithms in a worst case analysis with respect to classes of SDEs, which are defined in terms of smoothness constraints for the coefficients of the equation.
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  The Multi-Level Monte Carlo Technique for Approximation of Distribution Functions and an Application to AF4 By Prof. Klaus Ritter (Technische Universität Kaiserslautern, Germany)

  Prof. Klaus Ritter, Technische Universität Kaiserslautern

  Sep 16, 15:00 - 16:00

  B1 R4214

  The multi-level Monte Carlo approach is a powerful variance reduction technique, which is applied, in particular, in the context of SDEs. While the standard task is to compute the expectation of a real-valued functional, we discuss how to approximate a distribution function on a compact interval. In this talk, we establish upper bounds for the error of suitable multi-level algorithms.