Almost Sure Exponential Stability in the Numerical Simulation of Stochastic Differential Equations
Almost Sure Exponential Stability in the Numerical Simulation of Stochastic Differential Equations
This paper is mainly concerned with whether the almost sure exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical method. Under the global Lipschitz condition, we first show that the SDE is $p$th moment exponentially stable (for $p\in (0,1)$) if and only if the stochastic …