Download or read book Multilevel Monte Carlo Method for Parabolic Stochastic Partial Differential Equations written by Andrea Barth and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multilevel Monte Carlo Method with Applications to Stocastic Partial Differential Equations written by Andrea Barth and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2006 written by Alexander Keller and published by Springer Science & Business Media. This book was released on 2007-12-30 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.
Download or read book Monte Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2004 written by Harald Niederreiter and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas.
Download or read book Multilevel Monte Carlo Simulation for Stochastic Differential Equations Driven by L vy Processes written by Sangmeng Li and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Methods for Partial Differential Equations With Applications to Electronic Design Automation written by Wenjian Yu and published by Springer Nature. This book was released on 2022-09-02 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is one of the top 10 algorithms in the 20th century. This book is focusing on the Monte Carlo method for solving deterministic partial differential equations (PDEs), especially its application to electronic design automation (EDA) problems. Compared with the traditional method, the Monte Carlo method is more efficient when point values or linear functional of the solution are needed, and has the advantages on scalability, parallelism, and stability of accuracy. This book presents a systematic introduction to the Monte Carlo method for solving major kinds of PDEs, and the detailed explanation of relevant techniques for EDA problems especially the cutting-edge algorithms of random walk based capacitance extraction. It includes about 100 figures and 50 tables, and brings the reader a close look to the newest research results and the sophisticated algorithmic skills in Monte Carlo simulation software.
Download or read book Introduction to Monte Carlo Methods for Transport and Diffusion Equations written by Bernard Lapeyre and published by OUP Oxford. This book was released on 2003 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is used by for the resolution of partial differential equations, trasnport equations, the Boltzmann equation and the parabolic equations of diffusion.
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Bruno Tuffin and published by Springer Nature. This book was released on 2020-05-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Rennes, France, and organized by Inria, in July 2018. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
Download or read book Multilevel Monte Carlo Methods with Applications to Biochemical Models written by and published by . This book was released on 2015 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study multilevel Monte Carlo simulation methods and applications to different types of stochastic dynamical models. This dissertation focuses on three selected topics. Firstly, tau-leaping is a popular discretization method for generating approximate paths of continuous time, discrete space Markov chains, notably for biochemical reaction systems. To compute expected values in this context, an appropriate multilevel Monte Carlo form of tau-leaping has been shown to improve efficiency dramatically. The contribution for this topic is deriving new analytic results concerning the computational complexity of multilevel Monte Carlo tau-leaping that are significantly sharper than previous ones. The key feature of the analysis that allows for the sharper bounds is that when comparing relevant pairs of processes we analyze the vari- ance of their difference directly rather than bounding via the second moment. Secondly, we consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the small noise regime. Our complexity analysis shows multilevel Monte Carlo can improve on the complexity of standard Monte Carlo by a factor [epsilon], where [epsilon] is the desired accuracy. The take-home message is that, under reasonable assumptions, a basic Euler-Maruyama discretization leads to optimal asymptotic computational complexity when used in a multilevel setting. Thirdly, we analyze and compare the computational complexity of different simulation strategies for classically scaled continuous time Markov chains. We provide numerical examples demonstrating our main conclusions. The three topics have appeared in a series of three papers published or under review.
Download or read book Adaptive Multi Level Monte Carlo and Stochastic Collocation Methods for Hyperbolic Partial Differential Equations with Random Data on Networks written by Elisa Strauch and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Ronald Cools and published by Springer. This book was released on 2016-06-13 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.
Download or read book Monte Carlo and Quasi Monte Carlo Methods 2012 written by Josef Dick and published by Springer Science & Business Media. This book was released on 2013-12-05 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of New South Wales (Australia) in February 2012. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance, statistics and computer graphics.
Download or read book Numerical Methods for Stochastic Partial Differential Equations with White Noise written by Zhongqiang Zhang and published by Springer. This book was released on 2017-09-01 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Download or read book Monte Carlo and Quasi Monte Carlo Methods written by Art B. Owen and published by Springer. This book was released on 2018-07-03 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.
