Frontiers of Mathematics in China >
Stochastic Volterra equations driven by fractional Brownian motion
Received date: 02 Dec 2013
Accepted date: 01 Jul 2014
Published date: 01 Apr 2015
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This paper is devoted to study a class of stochastic Volterra equations driven by fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct application, we provide an alternative method to describe the regularities of the law of the solution. Secondly, by using the Malliavin calculus, the Bismut type derivative formula is established, which is then applied to the study of the gradient estimate and the strong Feller property. Finally, we establish the Talagrand type transportation cost inequalities for the law of the solution on the path space with respect to both the uniform metric and the L2-metric.
Xiliang FAN . Stochastic Volterra equations driven by fractional Brownian motion[J]. Frontiers of Mathematics in China, 2015 , 10(3) : 595 -620 . DOI: 10.1007/s11464-015-0413-y
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