Stochastic Partial Differential Equations With Additive Gaussian Noise Analysis And Inference
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Stochastic Partial Differential Equations With Additive Gaussian Noise Analysis And Inference
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Author : Ciprian A Tudor
language : en
Publisher: World Scientific
Release Date : 2022-10-11
Stochastic Partial Differential Equations With Additive Gaussian Noise Analysis And Inference written by Ciprian A Tudor and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-11 with Mathematics categories.
The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.
A Minicourse On Stochastic Partial Differential Equations
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Author : Robert C. Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
A Minicourse On Stochastic Partial Differential Equations written by Robert C. Dalang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.
Numerical Methods For Stochastic Partial Differential Equations With White Noise
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Author : Zhongqiang Zhang
language : en
Publisher: Springer
Release Date : 2017-09-01
Numerical Methods For Stochastic Partial Differential Equations With White Noise written by Zhongqiang Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-01 with Mathematics categories.
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.
Stochastic Partial Differential Equations
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Stochastic Partial Differential Equations written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in reservoir theory and related areas. 3) The theory should be strong and efficient enough to allow us to solve th,~se SPDEs explicitly, or at least provide algorithms or approximations for the solutions.
Stochastic Partial Differential Equations
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-01
Stochastic Partial Differential Equations written by Helge Holden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-01 with Mathematics categories.
The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher:
Release Date : 1992
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Stochastic Partial Differential Equations
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Author : Alison Etheridge
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13
Stochastic Partial Differential Equations written by Alison Etheridge and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-13 with Mathematics categories.
Consists of papers given at the ICMS meeting held in 1994 on this topic, and brings together some of the world's best known authorities on stochastic partial differential equations.
Stochastic Partial Differential Equations And Applications Ii
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Author : Giuseppe Da Prato
language : en
Publisher: Springer
Release Date : 2006-11-14
Stochastic Partial Differential Equations And Applications Ii written by Giuseppe Da Prato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Recent Development In Stochastic Dynamics And Stochastic Analysis
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Author : Jinqiao Duan
language : en
Publisher: World Scientific
Release Date : 2010
Recent Development In Stochastic Dynamics And Stochastic Analysis written by Jinqiao Duan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Hyperbolic equations with random boundary conditions / Zdzisław Brzeźniak and Szymon Peszat -- 2. Decoherent information of quantum operations / Xuelian Cao, Nan Li and Shunlong Luo -- 3. Stabilization of evolution equations by noise / Tomás Caraballo and Peter E. Kloeden -- 4. Stochastic quantification of missing mechanisms in dynamical systems / Baohua Chen and Jinqiao Duan -- 5. Banach space-valued functionals of white noise / Yin Chen and Caishi Wang -- 6. Hurst index estimation for self-similar processes with long-memory / Alexandra Chronopoulou and Frederi G. Viens -- 7. Modeling colored noise by fractional Brownian motion / Jinqiao Duan, Chujin Li and Xiangjun Wang -- 8. A sufficient condition for non-explosion for a class of stochastic partial differential equations / Hongbo Fu, Daomin Cao and Jinqiao Duan -- 9. The influence of transaction costs on optimal control for an insurance company with a new value function / Lin He, Zongxia Liang and Fei Xing -- 10. Limit theorems for p-variations of solutions of SDEs driven by additive stable Lévy noise and model selection for paleo-climatic data / Claudia Hein, Peter Imkeller and Ilya Pavlyukevich -- 11. Class II semi-subgroups of the infinite dimensional rotation group and associated Lie algebra / Takeyuki Hida and Si Si -- 12. Stopping Weyl processes / Robin L. Hudson -- 13. Karhunen-Loéve expansion for stochastic convolution of cylindrical fractional Brownian motions / Zongxia Liang -- 14. Stein's method meets Malliavin calculus : a short survey with new estimates / Ivan Nourdin and Giovanni Peccati -- 15. On stochastic integrals with respect to an infinite number of Poisson point process and its applications / Guanglin Rang, Qing Li and Sheng You -- 16. Lévy white noise, elliptic SPDEs and Euclidean random fields / Jiang-Lun Wu -- 17. A short presentation of Choquet integral / Jia-An Yan
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2002-04-05
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.