Stochastic Partial Differential Equations: An Introduction - Brossura

Pardoux, Etienne

Brossura

ISBN 10: 3030890023 ISBN 13: 9783030890025

Casa editrice: Springer Nature, 2021

Riassunto

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.

Su questo libro

Informazioni sull?autore

Etienne Pardoux is professor emeritus at the Institut de Mathématiques de Marseille, within Aix Marseille Univ. His research has covered several topics of stochastic analysis, in particular stochastic partial differential equations, backward stochastic differential equations and homogenization. More recently, he has turned his interests towards evolutionary biology and modeling of infectious diseases. He is the author of more than 160 publications, including four books.

 

Dalla quarta di copertina

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.

Dettagli dell?edizione

• Editore: Springer Nature
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 3030890023
• ISBN 13: 9783030890025
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 84
• Contatto del produttore: non disponibile