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Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation. (English) Zbl 1059.65006
The authors prove conditions under which the semi-implicit Euler method has strong order of convergence 1/2 for scalar, linear stochastic differential delay equations. They also investigate mean square stability in terms of the stepsize of the method and the problem parameters. Numerical results illustrate some of the theory.

65C30Stochastic differential and integral equations
60H10Stochastic ordinary differential equations
34F05ODE with randomness
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
60H35Computational methods for stochastic equations
Full Text: DOI
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