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.
Table of Contents:
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 Solutions. Further Applications. Diffusion Equations in Infinite Dimensions. Bibliography. Index.
Review :
"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
