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Zbl 1015.65002
Mao, Xuerong; Sabanis, Sotirios
Numerical solutions of stochastic differential delay equations under local Lipschitz condition. (English)
[J] J. Comput. Appl. Math. 151, No.1, 215-227 (2003). ISSN 0377-0427

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 $$dx(t)= f\biggl(x,\bigl( \delta(t)\bigr)\biggr) dt+g\biggl(x(t), x \bigl(\delta(t) \bigr)\biggr) dB(t)$$ where $B$ is an $m$-dimensional Brownian motion.
[Melvin D.Lax (Long Beach)]

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

Keywords: stochastic differential delay equations; local Lipschitz condition; Euler-Maruyama method; convergence; Brownian motion

Cited in: Zbl 1212.34252

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