Harnack inequalities for functional SDEs with multiplicative noise and applications

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Wang, Feng-Yu^1,2  Yuan, Chenggui² 

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

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

关键词: Harnack inequality;    Functional solution;    Delay SDE;    Strong Feller property;    Heat kernel;   

DOI  :  10.1016/j.spa.2011.07.001

来源: Elsevier

【 摘 要 】

By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong Feller property and heat kernel estimates w.r.t. quasi-invariant probability measures are derived for the associated transition semigroup of the solution. The dimension-free Harnack inequality in the sense of Wang (1997) [14] is also investigated. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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