Stochastic partial differential equations, space-time white noise and random fields Robert C. Dalang, Marta Sanz-Solé

Format:

Book

Author/Creator:

Dalang, Robert C., 1961- author.

Sanz Solé, Marta, 1952- author.

Series:

Springer monographs in mathematics

Springer monographs in mathematics 2196-9922

Language:

English

Subjects (All):

Stochastic partial differential equations.

Gaussian processes.

White noise theory.

Random fields.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Springer [2026]

Summary:

"This open access book provides a comprehensive introduction to the theory of stochastic partial differential equations (SPDEs). The focus is on SPDEs driven by Gaussian space-time white noise. The book covers both linear and nonlinear SPDEs, with Lipschitz and locally Lipschitz coefficients and multiplicative noise. It provides a modern presentation of the theory of stochastic integration with respect to space-time white noise and unifies many results in the literature. The book discusses fundamental topics such as existence and uniqueness of random field solutions, along with their space-time sample path regularity properties. The book also presents a selection of additional topics such as weak solutions in law to SPDEs, space-time Markov properties, asymptotic bounds on moments, comparison theorems, a study of polarity of points for SPDEs with additive noise, and a study of SPDEs with rough initial conditions that includes the parabolic and hyperbolic Anderson models and their intermittency properties. In the context of the stochastic heat equation, the book discusses additional important topics including invariant and limit measures, reversible measures and their relationship to bridge measures, irreducibility properties, and large interval asymptotics. The appendices gather results from analysis and stochastic processes that are used throughout the core of the book, including key elements from the general theory of stochastic processes, a detailed presentation of Kolmogorov’s anisotropic continuity criterion, numerous integrability properties of the fundamental solutions and Green's functions associated to the heat and wave partial differential operators, explicit calculations of some space-time convolution series and some useful Gronwall-type lemmas. The book aims to be a reference for established researchers in the field of SPDEs, as well as for those who are interested in entering the field and becoming familiar with its techniques. In particular, graduate and postgraduate students with a background in stochastic analysis will find here a comprehensive and self-contained source of information which provides essential expertise in the subject"-- Springer Nature Link

Contents:

Basics on noise and SPDEs

Stochastic integrals with respect to space-time white noise

Linear SPDEs driven by space-time white noise

Non-linear SPDEs driven by space-time white noise

Asymptotic behaviors in the stochastic heat equation

Notes:

Includes bibliographical references and indexes

Online resource; title from PDF title page (Springer Nature Link, viewed February 4, 2026)

Other Format:

Print version Stochastic partial differential equations, space-time white noise and random fields

ISBN:

9783032016508

3032016509

OCLC:

1570319405

Access Restriction:

Some versions Open access versions available from some providers open access