Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients

Surong You, Wei Mao, Xuerong Mao and Liangjian Hu

Applied Mathematics and Computation, 2015, vol. 263, issue C, 73-83

Abstract: This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

Keywords: Brownian motion; Markov chain; Hybrid pantograph stochastic differential equations; Exponential stability; Generalized Itô formula; Robust stability (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:263:y:2015:i:c:p:73-83

DOI: 10.1016/j.amc.2015.04.022

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