Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions

Twardowska, Krystyna

Książka - szczegóły

Tytuł książki

Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions

Autorzy

Krystyna Twardowska

Seria

Rozprawy Matematyczne tom/nr w serii: 325 wydano: 1993

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Pełne teksty:

http://matwbn.icm.edu.pl/ksiazki/rm/rm325/rm32501.pdf [zdalny]

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EN

CONTENTS
1. Introduction...........................................................................................................................................5
1.1. The Wong-Zakai theorem and its generalizations.............................................................................5
1.2. Approximation methods for stochastic differential equations.............................................................7
1.3. Extensions of the Wong-Zakai theorem and their applications..........................................................9
2. Approximation theorem of Wong-Zakai type for functional stochastic differential equations................10
2.1. Introductory remarks........................................................................................................................10
2.2. Definitions and notation...................................................................................................................10
2.3. Description of the model..................................................................................................................11
2.4. Approximation theorem....................................................................................................................15
2.5. Examples.........................................................................................................................................24
3. An extension of the Wong-Zakai theorem to stochastic evolution equations in Hilbert spaces............26
3.1. Introductory remarks.......................................................................................................................26
3.2. Definitions and notation..................................................................................................................26
3.3. Description of the model.................................................................................................................27
3.4. The main theorem...........................................................................................................................31
3.5. Examples.........................................................................................................................................41
  3.5.1. Equations satisfying the assumptions of Theorem 3.4.1.............................................................41
  3.5.2. Stochastic delay equations.........................................................................................................43
  3.5.3. Stochastic wave equations..........................................................................................................45
4. Comparison of the results...................................................................................................................46
4.1. Finite-dimensional case..................................................................................................................46
4.2. Stochastic delay equations.............................................................................................................47
5. On the relation between the Itô and Stratonovich integrals in Hilbert spaces.....................................47
6. Conclusions........................................................................................................................................49
References.............................................................................................................................................50

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 325

Liczba stron

54

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, CCCXXV

Daty

wydano

1993

otrzymano

1992-03-27

poprawiono

1992-07-13

Twórcy

autor

Krystyna Twardowska

Institute of Mathematics, Warsaw Technical University, Pl. Politechniki 1, 00-661 Warszawa, Poland

Bibliografia

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1991 Mathematics Subject Classification: 34G20, 34K50, 35R15, 60H05, 60H10, 60H15, 60H30.

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Książka - szczegóły

Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions

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