Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions: monograph

Research output: Book/ReportBookResearchpeer-review

Abstract

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.
The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Original languageEnglish
Place of PublicationBoca Raton
PublisherCRC Press
Number of pages286
ISBN (Print)978-1-4822-1050-7
Publication statusPublished - 2016

Publication series

NameChapman & Hall/CRC Monographs and Research Notes in Mathematics
PublisherCRC Press

Fingerprint

Infinite Dimensions
Cauchy Problem
Semigroup
Stochastic Analysis
Dimensional Analysis
Generalized Solution
Random process
White noise
Stochastic Equations
Regularization
Integral Equations
Hilbert space
Cover
Differential equation

Cite this

MELNIKOVA, I. V. (2016). Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions: monograph. (Chapman & Hall/CRC Monographs and Research Notes in Mathematics). Boca Raton: CRC Press.
MELNIKOVA, I.V. / Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions : monograph. Boca Raton : CRC Press, 2016. 286 p. (Chapman & Hall/CRC Monographs and Research Notes in Mathematics).
@book{0f57edae2a614f4b988da2f7e6131596,
title = "Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions: monograph",
abstract = "Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the {"}classical{"} approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.",
author = "I.V. MELNIKOVA",
year = "2016",
language = "English",
isbn = "978-1-4822-1050-7",
series = "Chapman & Hall/CRC Monographs and Research Notes in Mathematics",
publisher = "CRC Press",

}

MELNIKOVA, IV 2016, Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions: monograph. Chapman & Hall/CRC Monographs and Research Notes in Mathematics, CRC Press, Boca Raton.

Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions : monograph. / MELNIKOVA, I.V.

Boca Raton : CRC Press, 2016. 286 p. (Chapman & Hall/CRC Monographs and Research Notes in Mathematics).

Research output: Book/ReportBookResearchpeer-review

TY - BOOK

T1 - Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions

T2 - monograph

AU - MELNIKOVA, I.V.

PY - 2016

Y1 - 2016

N2 - Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

AB - Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

UR - https://elibrary.ru/item.asp?id=29273070

M3 - Book

SN - 978-1-4822-1050-7

T3 - Chapman & Hall/CRC Monographs and Research Notes in Mathematics

BT - Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions

PB - CRC Press

CY - Boca Raton

ER -

MELNIKOVA IV. Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions: monograph. Boca Raton: CRC Press, 2016. 286 p. (Chapman & Hall/CRC Monographs and Research Notes in Mathematics).