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

Miao Wang, Jiang-lun Wu Orcid Logo

Frontiers of Mathematics in China, Volume: 9, Issue: 3, Pages: 601 - 622

Swansea University Author: Jiang-lun Wu Orcid Logo

DOI (Published version): 10.1007/s11464-014-0364-8

Abstract

Based on a recent result on linking stochastic differential equations on ℝ 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...

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Published in: Frontiers of Mathematics in China
Published: 2014
Online Access: http://link.springer.com/article/10.1007%2Fs11464-014-0364-8
URI: https://cronfa.swan.ac.uk/Record/cronfa22315
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Abstract: Based on a recent result on linking stochastic differential equations on ℝ 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, path-independence
College: Faculty of Science and Engineering
Issue: 3
Start Page: 601
End Page: 622

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