Stochastic Pdes And Dynamics

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Stochastic Pdes And Dynamics
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Author : Boling Guo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-11-21
Stochastic Pdes And Dynamics written by Boling Guo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-21 with Mathematics categories.
This book explains mathematical theories of a collection of stochastic partial differential equations and their dynamical behaviors. Based on probability and stochastic process, the authors discuss stochastic integrals, Ito formula and Ornstein-Uhlenbeck processes, and introduce theoretical framework for random attractors. With rigorous mathematical deduction, the book is an essential reference to mathematicians and physicists in nonlinear science. Contents: Preliminaries The stochastic integral and Itô formula OU processes and SDEs Random attractors Applications Bibliography Index
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 An Introduction
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Author : Wei Liu
language : en
Publisher: Springer
Release Date : 2015-10-06
Stochastic Partial Differential Equations An Introduction written by Wei Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-06 with Mathematics categories.
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the well-known case of globally monotone coefficients, substantially widens the applicability of the results.
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.
Random Perturbation Of Pdes And Fluid Dynamic Models
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Author : Franco Flandoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-11
Random Perturbation Of Pdes And Fluid Dynamic Models written by Franco Flandoli 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 2011-03-11 with Mathematics categories.
This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.
Stochastic Optimal Control In Infinite Dimension
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Author : Giorgio Fabbri
language : en
Publisher: Springer
Release Date : 2017-06-22
Stochastic Optimal Control In Infinite Dimension written by Giorgio Fabbri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Mathematics categories.
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Stochastic Dynamics In Computational Biology
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Author : Stefanie Winkelmann
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Stochastic Dynamics In Computational Biology written by Stefanie Winkelmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.
The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
An Introduction To Computational Stochastic Pdes
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Author : Gabriel J. Lord
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-11
An Introduction To Computational Stochastic Pdes written by Gabriel J. Lord 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 2014-08-11 with Business & Economics categories.
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
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 Control Theory
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Author : Makiko Nisio
language : en
Publisher: Springer
Release Date : 2014-11-27
Stochastic Control Theory written by Makiko Nisio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.