Open AccessExistence and Ulam-Hyers-Rassias stability of stochastic differential equations with random impulses
Author(s) -
Wenxuan Lang,
Sufang Deng,
Xu Shu,
Fei Xu
Publication year - 2021
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/fil2102399l
Subject(s) - mathematics , stability (learning theory) , stochastic differential equation , gronwall's inequality , fixed point , fixed point theorem , differential equation , type (biology) , mathematical analysis , inequality , computer science , ecology , machine learning , biology
In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii?s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.