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Stochastic Volterra equations driven by fractional Brownian motion
Authors:Xiliang FAN
Institution:1. Department of Statistics, Anhui Normal University, Wuhu 241003, China2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Abstract: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.
Keywords:Fractional Brownian motion  derivative formula  integration by parts formula  stochastic Volterra equation  Malliavin calculus  
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