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Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. (English) Zbl 1144.65005
The authors study the ability of numerical methods for stochastic differential equations to reproduce almost sure and small-moment stability. They find conditions under which the Euler-Maruyama method preserves stability properties for small timesteps. They investigate the backward Euler method and the stochastic theta method as well.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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