Stochastic Volterra equations driven by fractional Brownian motion

作     者：Xiliang FAN 

作者机构：Department of Statistics Anhui Normal University Wuhu 241003 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2015年第10卷第3期

页      面：595-620页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Acknowledgements The author would like to thank Professor Feng-Yu Wang for his encouragement and comments that have led to improvements of the manuscript and the referees for helpful comments and corrections. This work was supported in part by the Research Project of Natural Science Foundation of Anhui Provincial Universities (Grant No. K32013A134)  the Natural Science Foundation of Anhui Province (Grant No. 1508085QA03)  and the National Natural Science Foundation of China (Grant No. 11371029) 

主　　题：Fractional Brownian motion derivative formula integration byparts formula stochastic Volterra equation Malliavin calculus 

摘      要：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 L^2-metric.