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

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Swansea University, Swansea, SA2 8PP, UK

    Miao Wang & Jiang-Lun Wu

  2. School of Mathematics, Northwest University, Xi’an, 710127, China

    Jiang-Lun Wu

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  1. Miao Wang
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  2. Jiang-Lun Wu
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Correspondence to Jiang-Lun Wu.

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Wang, M., Wu, JL. Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations. Front. Math. China 9, 601–622 (2014). https://doi.org/10.1007/s11464-014-0364-8

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