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Zbl 1144.65005
Higham, Desmond J.; Mao, Xuerong; Yuan, Chenggui
Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations. (English)
[J] SIAM J. Numer. Anal. 45, No. 2, 592-609 (2007). ISSN 0036-1429; ISSN 1095-7170/e

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.
[Grigori N. Milstein (Ekaterinburg)]

MSC 2000:: *65C30 Stochastic differential and integral equations
60H10 Stochastic ordinary differential equations
60H35 Computational methods for stochastic equations
34F05 ODE with randomness
65L20 Stability of numerical methods for ODE
65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: one-sided Lipschitz condition; linear growth condition; Lyapunov exponent; stochastic theta method; stochastic differential equations; Euler-Maruyama method; stability; backward Euler method

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