Harnack inequalities for stochastic equations driven by Levy noise

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Wang, Feng-Yu^1,3  Wang, Jian² 

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Peoples R China

[3] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

关键词: Harnack inequality;    Coupling;    Levy process;    Subordinator;   

DOI  :  10.1016/j.jmaa.2013.08.013

来源: Elsevier

【 摘 要 】

By using coupling argument and regularization approximations of the underlying sub-ordinator, dimension-free Harnack inequalities are established for a class of stochastic equations driven by a Levy noise containing a subordinate Brownian motion. The Harnack inequalities are new even for linear equations driven by Levy noise, and the gradient estimate implied by our log-Harnack inequality considerably generalizes some recent results on gradient estimates and coupling properties derived for Levy processes or linear equations driven by Levy noise. The main results are also extended to semilinear stochastic equations in Hilbert spaces. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free