# Almost Sure Exponential Stability in the Numerical Simulation of Stochastic Differential Equations

@article{Mao2015AlmostSE,
title={Almost Sure Exponential Stability in the Numerical Simulation of Stochastic Differential Equations},
author={Xuerong Mao},
journal={SIAM J. Numerical Analysis},
year={2015},
volume={53},
pages={370-389}
}
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 theta method is $p$th moment exponentially stable for a sufficiently small step size. We then show that the $p$th moment exponential stability of the SDE or the stochastic theta… CONTINUE READING

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