Relatively compact families of functionals on abstract Wiener space and applications

Xicheng Zhang

doi:10.1016/j.jfa.2005.06.016

Relatively compact families of functionals on abstract Wiener space and applications

Xicheng Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper we prove two relatively compact criterions in some L^p-spaces(p > 1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.

Original language	English
Pages (from-to)	195-221
Number of pages	27
Journal	Journal of Functional Analysis
Volume	232
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2005.06.016
Publication status	Published - 1 Mar 2006
Externally published	Yes

Keywords

Malliavin calculus
Relatively compact criterion
Stochastic differential equation
Stochastic partial differential equation
Wiener-Sobolev space

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10.1016/j.jfa.2005.06.016

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AB - In this paper we prove two relatively compact criterions in some Lp-spaces(p > 1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.

KW - Malliavin calculus

KW - Relatively compact criterion

KW - Stochastic differential equation

KW - Stochastic partial differential equation

KW - Wiener-Sobolev space

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Relatively compact families of functionals on abstract Wiener space and applications

Abstract

Keywords

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