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Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations
Frontiers of Mathematics in China, Volume: 9, Issue: 3, Pages: 601 - 622
Swansea University Author:
Jiang-lun Wu
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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...
Published in: | Frontiers of Mathematics in China |
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Published: |
2014
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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. |
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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 |