{"title":"Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps","authors":"Dezhi Liu","volume":54,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":908,"pagesEnd":912,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6075","abstract":"
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.<\/p>\r\n","references":"[1] Zhang Q Q. On a linear delay difference equation with impulses.\r\nAnn.Differential Equations,2002,18:197-204.\r\n[2] Braverman E. On a discrete model of population dynamics with impulsive\r\nharvesting or recruitment. Nonlinear Anal.,2005,63(5):751-759.\r\n[3] Wei G P. The persistence of nonoscillatory solutions\r\nof difference equations under impulsive perturbations.\r\nComput.andMath.Appl.,2005,50(10):1579-1586.\r\n[4] Peng M S. Oscillation criteria for second-order impulsive delay difference\r\nequations. Appl.Math.Comput., 2003,146(1):227-235.\r\n[5] Mao X. Stability of stochastic differential equations with respect to\r\nsemimartingales. NewYork:Longman Scientific and Technical,1991.\r\n[6] Luo J W. Comparison principle and stability of Ito stochastic differential\r\ndelay equations with poisson jumps and Markovian swithching. Nonlinear\r\nAnalysis,2006,64:253-262.\r\n[7] Mao X. Exponential stability of stochastic differential equations.\r\nNewYork:Marcel Dekker, 1994.\r\n[8] Mao X. Stochastic differential equations and applications.\r\nNewYork:Horwood,1997.\r\n[9] Li R H. Convergence of numerical solutions to stochastic delay differential\r\nequations with jumps. App.Math.Comp.,2006,172(2):584-602.\r\n[10] Yang Z, Xu D. Mean square exponential stability of impulsive stochastic\r\ndifference equations. Appl.math.Letter,2007,20:938-945.\r\n[11] Yang J, Zhong S. Mean square stability of impulsive stochastic differential\r\nequations with delays. J.comp.appl.math.,in press.\r\n[12] Yang Z, Xu D. Exponential p-stability of impulsive stochastic differential\r\nequations with delays. Physics Letters A,2006,359(3):129-137.\r\n[13] Wu S. The Euler scheme for random impulsive differential equations.\r\nAppl.math.comp.,in press.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 54, 2011"}