Numerical analysis of explicit one-step methods for stochastic delay differential equations. (English) Zbl 0974.65008
Summary: We consider the problem of strong approximations of the solution of stochastic differential equations of Itô form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler-Maruyama scheme.
MSC:
65C30 | Numerical solutions to stochastic differential and integral equations |
34K50 | Stochastic functional-differential equations |
65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential 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 |
Keywords:
stochastic delay differential equations; convergence; one-step methods; numerical examples; Euler-Maruyama schemeReferences:
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