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Numerical solutions of stochastic differential delay equations under local Lipschitz condition. (English) Zbl 1015.65002

Under certain hypotheses, which include the less restrictive assumption that f,g satisfy a local (rather than global) Lipschitz condition, a theorem is proved establishing convergence of Euler-Maruyama approximate solutions to the solution of the stochastic differential delay equation with variable delay

dx(t)=fx , δ ( t )dt+gx (t) , x δ ( t )dB(t)

where B is an m-dimensional Brownian motion.


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