Harnack inequalities for functional SDEs with multiplicative noise and applications
AbstractBy 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)  is also investigated.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 11 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Arnaudon, Marc & Thalmaier, Anton & Wang, Feng-Yu, 2009. "Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3653-3670, October.
- Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.
- Zhang, Shao-Qin, 2013. "Harnack inequality for semilinear SPDE with multiplicative noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1184-1192.
- Wang, Feng-Yu & Zhang, Tusheng, 2014. "Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1261-1274.
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