Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Blouhi, T.; Caraballo, T.; Ouahab, A.
• Is Part Of: Stochastic analysis and applications. Volume 34:Issue 5(2016)
• Page Start: 792
• Page End: 834
• Publication Date: 2016-09-02
• Subjects: Mild solutions -- fractional Brownian motion -- impulsive differential equations -- matrix convergent to zero -- generalized Banach space -- fixed point; 34A37 -- 60H99 -- 47H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1180994
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations with infinite fractional Brownian motions are proved. The approach is based on Perov's fixed point theorem and a new version of Schaefer's fixed point theorem in generalized Banach spaces. The relationship between mild and weak solutions and the exponential stability of mild solutions are investigated as well. The abstract theory is illustrated with an example.