Averaging principle and stability of hybrid stochastic fractional differential equations driven by Lévy noise. Issue 12 (9th September 2020)

• Record Type: Journal Article
• Authors: Shen, Guangjun; Xiao, Ruidong; Yin, Xiuwei
• Is Part Of: International journal of systems science. Volume 51:Issue 12(2020)
• Page Start: 2115
• Page End: 2133
• Publication Date: 2020-09-09
• Subjects: Stochastic fractional differential equations -- Lévy noise -- Markovian switching -- averaging principle -- stability; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2020.1784493
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : Stability of stochastic differential equations driven by Lévy noise with Markovian switching has recently received a lot of attention. Different from the integer-order stochastic differential equations, stochastic fractional differential equations play a circular role in describing many practical processes and systems. In this paper, our aims are to study the averaging principle of the solution of hybrid stochastic fractional differential equations driven by Lévy noise under non-Lipschitz conditions which include classical Lipschitz conditions as special cases and propose several sufficient conditions for asymptotic stability in the p th moment of the solution. Two examples with numerical simulation are given to illustrate the obtained theory.