Stochastic Partial Differential Equations
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Stochastic Partial Differential Equations Second Edition
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Author : Pao-Liu Chow
language : en
Publisher: CRC Press
Release Date : 2014-12-10
Stochastic Partial Differential Equations Second Edition written by Pao-Liu Chow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-10 with Mathematics categories.
Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
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 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.
Stochastic Partial Differential Equations
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Author : Étienne Pardoux
language : en
Publisher: Springer Nature
Release Date : 2021-10-25
Stochastic Partial Differential Equations written by Étienne Pardoux and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.
This book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Itô formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Hölder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and their connection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory.
A Concise Course On Stochastic Partial Differential Equations
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Author : Claudia Prévôt
language : en
Publisher: Springer
Release Date : 2007-05-26
A Concise Course On Stochastic Partial Differential Equations written by Claudia Prévôt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Stochastic Ordinary And Stochastic Partial Differential Equations
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Author : Peter Kotelenez
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-05
Stochastic Ordinary And Stochastic Partial Differential Equations written by Peter Kotelenez 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 2007-12-05 with Mathematics categories.
Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
A Concise Course On Stochastic Partial Differential Equations
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Author : Claudia Prévôt
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-08
A Concise Course On Stochastic Partial Differential Equations written by Claudia Prévôt 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 2007-06-08 with Mathematics categories.
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Stochastic Partial Differential Equations Six Perspectives
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Author : René Carmona
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Stochastic Partial Differential Equations Six Perspectives written by René Carmona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR
Stochastic Partial Differential Equations
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Author : Sergey V. Lototsky
language : en
Publisher: Springer
Release Date : 2017-07-06
Stochastic Partial Differential Equations written by Sergey V. Lototsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.