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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.

MSC:

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