New regularity of kolmogorov equation and application on approximation of semi-linear spdes with Hölder continuous drifts

Jianhai Bao; Xing Huang; Chenggui Yuan

doi:10.3934/cpaa.2019018

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2019, Volume 18, Issue 1: 341-360. Doi: 10.3934/cpaa.2019018

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New regularity of kolmogorov equation and application on approximation of semi-linear spdes with Hölder continuous drifts

1.
Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
2.
Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, United Kingdom

* Corresponding author
* Corresponding author

Received: December 31, 2017

Revised: March 31, 2018

Published: August 2018

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Abstract

In this paper, some new results on the the regularity of Kolmogorov equations associated to the infinite dimensional OU-process are obtained. As an application, the average $L^2$-error on $[0, T]$ of exponential integrator scheme for a range of semi-linear stochastic partial differential equations is derived, where the drift term is assumed to be Hölder continuous with respect to the Sobolev norm $\|·\|_{β}$ for some appropriate $β>0$. In addition, under a stronger condition on the drift, the strong convergence estimate is obtained, which covers the result of the SDEs with Hölder continuous drift.

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Mathematics Subject Classification: Primary: 60H15, 35R60, 65C30.

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