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

You, Surong and Mao, Wei and Mao, Xuerong and Hu, Liangjian (2015) Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients. Applied Mathematics and Computation, 263. 73–83. ISSN 0096-3003

[img]
Preview
Text (You-etal-AMC-2015-Analysis-on-Exponential-stability-of-hybrid-pantograph-stochastic-differential-equations)
You_etal_AMC_2015_Analysis_on_Exponential_stability_of_hybrid_pantograph_stochastic_differential_equations.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (313kB)| Preview

    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.