Stochastic Volterra equations driven by fractional Brownian motion

doi:10.1007/s11464-015-0413-y

Front. Math. China

2015, Vol. 10

Issue (3) : 595-620 https://doi.org/10.1007/s11464-015-0413-y

RESEARCH ARTICLE

Stochastic Volterra equations driven by fractional Brownian motion

Xiliang FAN^1,^2,^*(

)

1. Department of Statistics, Anhui Normal University, Wuhu 241003, China
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

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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

Corresponding Author(s): Xiliang FAN

Issue Date: 01 April 2015

Cite this article:

Xiliang FAN. Stochastic Volterra equations driven by fractional Brownian motion[J]. Front. Math. China, 2015, 10(3): 595-620.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0413-y
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I3/595

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