论文信息 - Exponential stability for stochastic differential equation driven by G-Brownian motion

Exponential stability for stochastic differential equation driven by G-Brownian motion

Consider a stochastic differential equation driven by G-Brownian motion dX(t)=AX(t)dt+σ(t,X(t))dBt which might be regarded as a stochastic perturbed system of dX(t)=AX(t)dt. Suppose the second equation is quasi surely exponentially stable. In this paper, we investigate the sufficient conditions under which the first equation is still quasi surely exponentially stable.

Defei Zhang | Zengjing Chen | Zengjing Chen | Defei Zhang

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

[2] Shige Peng,et al. Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths , 2008, 0802.1240.

[3] Xuerong Mao,et al. LEBESGUE-STIELTJES INTEGRAL INEQUALITIES AND STOCHASTIC STABILITIES , 1989 .

[4] S. Peng. G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type , 2006, math/0601035.

[5] Etienne Pardoux,et al. Almost sure and moment stability for linear ito equations , 1986 .

[6] Zengjing Chen,et al. Strong laws of large numbers for capacities , 2010 .

[7] Hui Jiang,et al. Large deviations for stochastic differential equations driven by G-Brownian motion , 2010 .

[8] R. Khas'minskii,et al. Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems , 1967 .