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

Surong You, Wei Mao, Xuerong Mao, Liangjian Hu

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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.
Original languageEnglish
Pages (from-to)73–83
Number of pages11
JournalApplied Mathematics and Computation
Volume263
Early online date21 May 2015
DOIs
Publication statusPublished - 15 Jul 2015

Keywords

  • Brownian motion
  • Markov chain
  • hybrid pantograph stochastic differential equations
  • exponential stability
  • robust stability

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