Stochastic Partial Differential Equations

Zusatztext "This is the second edition of the very well-written and introductory! application-oriented book on stochastic partial differential equations (SPDEs) by P.L. Chow. Compared to the first edition! the main change is adding new materials about SPDEs driven by Lévy-type noise."-Zentralblatt MATH 1321Praise for the First Edition:"The book provides an excellent introduction to the theory of stochastic partial differential equations ? a well-written and timely contribution to the literature." -Evelyn Buckwar! Zentralblatt Math! 2009"? an excellent guide to current research topics that opens possibilities for further developments in the field."-EMS Newsletter! 2008"This introductory book fills a gap in the field."-Nikita Y. Ratanov! Mathematical Reviews! 2008d"? very well-written introductory book ? I thoroughly recommend this book and believe that it will be a useful textbook with which to introduce students and young scientists to computational and analytical techniques for stochastic differential equations. This book is of great interest to applied mathematicians! theoretical physicists! naturalists! and all interested in the statistical formulation of scientific problems." -Andrzej Icha! Pure and Applied Geophysics! June 2005 Klappentext 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 Levy 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 Levy 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. Zusammenfassung 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 linea...

"This is the second edition of the very well-written and introductory, application-oriented book on stochastic partial differential equations (SPDEs) by P.L. Chow. Compared to the first edition, the main change is adding new materials about SPDEs driven by Lévy-type noise."Zentralblatt MATH 1321 Praise for the First Edition:"The book provides an excellent introduction to the theory of stochastic partial differential equations a well-written and timely contribution to the literature." Evelyn Buckwar, Zentralblatt Math, 2009 " an excellent guide to current research topics that opens possibilities for further developments in the field."EMS Newsletter, 2008 "This introductory book fills a gap in the field."Nikita Y. Ratanov, Mathematical Reviews, 2008d " very well-written introductory book I thoroughly recommend this book and believe that it will be a useful textbook with which to introduce students and young scientists to computational and analytical techniques for stochastic differential equations. This book is of great interest to applied mathematicians, theoretical physicists, naturalists, and all interested in the statistical formulation of scientific problems." Andrzej Icha, Pure and Applied Geophysics, June 2005

Autorentext
Pao-Liu Chow

Klappentext
This book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. This second edition incorporates new material concerning stochastic PDEs driven by Lévy-type noise. It includes new sections on stochastic differential equations of Lévy type as well as stochastic parabolic, hyperbolic, and evolution equations with Poisson noise. This edition also provides new applications of stochastic PDEs to population biology and finance and an updated section on parabolic equations and related elliptic problems in Gauss Sobolev spaces.

Zusammenfassung
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 GaussSobolev 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.

Inhalt
Preliminaries. Scalar Equations of First Order. Stochastic Parabolic Equations. Stochastic Parabolic Equations in the Whole Space. Stochastic Hyperbolic Equations. Stochastic Evolution Equations in Hilbert Spaces. Asymptotic Behavior of S…

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