Open AccessStochastic Volterra integro-differential equations driven by a fractional Brownian motion with delayed impulses
Author(s) -
Xia Zhou,
Xinzhi Liu,
Shouming Zhong
Publication year - 2017
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1719965z
Subject(s) - mathematics , fractional brownian motion , uniqueness , hurst exponent , fixed point theorem , brownian motion , mathematical analysis , stochastic differential equation , volterra integral equation , differential equation , integral equation , statistics
In this paper, the problem of existence of mild solutions for a stochastic Volterra integrodifferential equation with delayed impulses and driven by a fractional Brownian motion (Hurst parameter H ? (1/2,1)) is investigated. Here, we assume that the delayed impulses are linear and impulsive transients depend on not only their current but also historical states of the system. Utilizing the fixed point theorem combine with fractional power of operators and the semi-group theory, sufficient conditions that guarantee the existence and uniqueness of mild solutions for such equation are obtained. Finally, an example is presented to demonstrate the effectiveness of the proposed results.