Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations

doi:10.1007/s11464-014-0364-8

Front. Math. China

2014, Vol. 9

Issue (3) : 601-622 https://doi.org/10.1007/s11464-014-0364-8

RESEARCH ARTICLE

Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations

Miao WANG¹,Jiang-Lun WU^1,²(

)

1. Department of Mathematics, Swansea University, Swansea SA2 8PP, UK
2. School of Mathematics, Northwest University, Xi’an 710127, China

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Abstract

Based on a recent result on linking stochastic differential equations on ?d to (finite-dimensional) Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensional stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.

Keywords Characterization theorem Burgers-KPZ type nonlinear equations in infinite dimensions infinite-dimensional semi-linear stochastic differential equations Galerkin approximation Girsanov transformation stochastic heat equation path-independence Fréchet differentiation

Issue Date: 24 June 2014

Cite this article:

Miao WANG,Jiang-Lun WU. Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations[J]. Front. Math. China, 2014, 9(3): 601-622.

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https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0364-8
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I3/601

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