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Stability Analysis of Highly Nonlinear Hybrid Multiple-delay Stochastic Differential Equations
Chen Fei,Weiyin Fei,Xuerong Mao,Mingxuan Shen,Litan Yan
Keywords:variable multiple-delay stochastic differential equation; nonlinear growth condition; asymptotic stability; Markovian switching; Lyapunov functional.
Abstract:
      Stability criteria for stochastic differential delay equation (SDDE) have been studied intensively for the past few decades. However, most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability of highly nonlinear hybrid stochastic differential equations with a single delay is investigated in [Fei, Hu, Mao and Shen, Automatica, 2017], whose work, in this paper, is extended to highly nonlinear hybrid stochastic differential equations with variable multiple delays. In other words, this paper establishes the stability criteria of highly nonlinear hybrid variable multiple-delay stochastic differential equations. We also discuss an example to illustrate our results.