Stochastic Partial Differential Equations / Edition 1

by Pao-Liu Chow

Overview

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and Itô's equations, highlighting several computational and analytical techniques.

Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way. The author first brings the subject back to its root in classical concrete problems. He then discusses a unified theory of stochastic evolution equations and describes a few applied problems, including the random vibration of a nonlinear elastic beam and invariant measures for stochastic Navier-Stokes equations. The book concludes by pointing out the connection of stochastic PDEs to infinite-dimensional stochastic analysis.

By thoroughly covering the concepts and applications of stochastic PDEs at an introductory level, this text provides a guide to current research topics and lays the groundwork for further study.

Product Details

ISBN-13:	9780367453121
Publisher:	CRC Press
Publication date:	11/25/2019
Pages:	281
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Pau-Liu Chow

Table of Contents

Preface. 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. References. Index.

Editorial Reviews

"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

From the Publisher