论文信息 - The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points

The stability of neutral stochastic delay differential equations with Poisson jumps by fixed points

In the paper, the asymptotic mean square stability of the zero solution for neutral stochastic delay differential equations with Poisson jumps is studied by fixed points theory without Lyapunov functions. The coefficient functions have not been asked for a fixed sign, and the sufficient condition for mean square stability has been obtained. Therefore, some well-known results are improved and generalized.

Wei Zhang | Dezhi Liu | Guiyuan Yang

[1] X. Mao. Stability of Stochastic Differential Equations With Respect to Semimartingales , 1991 .

[2] X. Mao,et al. Exponential Stability of Stochastic Di erential Equations , 1994 .

[3] Li Ronghua,et al. Convergence of numerical solutions to stochastic delay differential equations with jumps , 2006 .

[4] T. A. Burton,et al. Perron-type stability theorems for neutral equations , 2003 .

[5] Jiaowan Luo. Fixed points and stability of neutral stochastic delay differential equations , 2007 .

[6] T. A. Burton,et al. Fixed points and stability of a nonconvolution equation , 2004 .

[7] Jiaowan Luo,et al. Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switching , 2006 .

[8] Bo Zhang,et al. Fixed points and stability of an integral equation: nonuniqueness , 2004, Appl. Math. Lett..

[9] X. Mao,et al. Stochastic Differential Equations and Applications , 1998 .

[10] Bo Zhang,et al. Fixed points and stability in differential equations with variable delays , 2005 .