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

• Main Authors: Issaka Louk-Man, Diop Mamadou Abdoul, Hmoyed Hasna
• Format: Article
• Language: English
• Published: De Gruyter 2020-10-01
• Series: Open Mathematics
• Subjects: resolvent operators; c0-semigroup; stochastic functional integro-differential equations; nonlocal condition; fractional brownian motion; mild solutions; 47h10; 47h09; 60g22; 35r12
• Online Access: https://doi.org/10.1515/math-2020-0063
• ISSN: 2391-5455

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.