Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps
Authors: Dezhi Liu
In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062232Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1258
 Zhang Q Q. On a linear delay difference equation with impulses. Ann.Differential Equations,2002,18:197-204.
 Braverman E. On a discrete model of population dynamics with impulsive harvesting or recruitment. Nonlinear Anal.,2005,63(5):751-759.
 Wei G P. The persistence of nonoscillatory solutions of difference equations under impulsive perturbations. Comput.andMath.Appl.,2005,50(10):1579-1586.
 Peng M S. Oscillation criteria for second-order impulsive delay difference equations. Appl.Math.Comput., 2003,146(1):227-235.
 Mao X. Stability of stochastic differential equations with respect to semimartingales. NewYork:Longman Scientific and Technical,1991.
 Luo J W. Comparison principle and stability of Ito stochastic differential delay equations with poisson jumps and Markovian swithching. Nonlinear Analysis,2006,64:253-262.
 Mao X. Exponential stability of stochastic differential equations. NewYork:Marcel Dekker, 1994.
 Mao X. Stochastic differential equations and applications. NewYork:Horwood,1997.
 Li R H. Convergence of numerical solutions to stochastic delay differential equations with jumps. App.Math.Comp.,2006,172(2):584-602.
 Yang Z, Xu D. Mean square exponential stability of impulsive stochastic difference equations. Appl.math.Letter,2007,20:938-945.
 Yang J, Zhong S. Mean square stability of impulsive stochastic differential equations with delays. J.comp.appl.math.,in press.
 Yang Z, Xu D. Exponential p-stability of impulsive stochastic differential equations with delays. Physics Letters A,2006,359(3):129-137.
 Wu S. The Euler scheme for random impulsive differential equations. Appl.math.comp.,in press.