Results on nonlocal stochastic integro-differential equations driven by a fractional Brownian motion

Abstract

This paper deals with the existence of mild solutions for a class of non-local stochastic integro-differential equations driven by a fractional Brownian motion with Hurst parameter H∈12,1H\in \left(\tfrac{1}{2},1\right). Discussions are based on resolvent operators in the sense of Grimmer, stochastic analysis theory and fixed-point criteria. As a final point, an example is given to illustrate the effectiveness of the obtained theory.

Keywords

• resolvent operators
• c0-semigroup
• stochastic functional integro-differential equations
• nonlocal condition
• fractional brownian motion
• mild solutions
• 47h10
• 47h09
• 60g22
• 35r12