Stochastic Volterra integro-differential equations driven by fractional Brownian motion in a Hilbert space

Abstract

In this article, we consider a class of stochastic Volterra integro-differential equations with infinite delay and impulsive effects, driven by fractional Brownian motion with the Hurst index in a Hilbert space. The cases of Lipschitz and bounded impulses are studied separately. The existence and uniqueness of mild solutions are proved by using different fixed-point theorems. An example is given to illustrate the theory.

Keywords::

• fractional Brownian motion
• Volterra equations
• mild solutions
• impulses
• infinite delays

2000 AMS Classification number::

• 60H15
• 60G22
• 45D05

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments which led to improvement of this work.