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题名/责任者:

Stochastic partial differential equations with additive Gaussian noise : analysis and inference / Ciprian A. Tudor.

出版发行项:

New Jersey : World Scientific Publishing Co., [2023]

ISBN:

9789811264450

载体形态项:

xi, 192 pages ; 24 cm

翻译题名:

鍔犳€ч珮鏂櫔澹伴殢鏈哄亸寰垎鏂圭▼锛氬垎鏋愬拰鎺ㄧ悊

个人责任者:

Tudor, Ciprian, 1973- author.

论题主题:

Stochastic partial differential equations.

论题主题:

Random noise theory.

论题主题:

Gaussian processes.

论题主题:

Heat equation.

论题主题:

Wave equation.

中图法分类号:

O211.63

书目附注:

Includes bibliographical references (pages 189-192).

内容附注:

Gaussian processes -- Fractional and Bifractional Brownian motion -- Multiparameter Gaussian processes -- Isonormal processes and Wiener integral -- The stochastic heat equation with space-time white noise -- The stochastic heat equation with correlated noise in space -- The stochastic wave equation with space-time white noise -- Variations of the solution to the stochastic heat equation -- Parameter estimation for the stochastic heat equation via power variations -- Power variations and inference for stochastic the wave equation.

摘要附注:

"The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation. The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space. The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed"--

豆瓣简介：