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The improved split-step backward Euler method for stochastic differential delay equations. (English) Zbl 1235.65010

The authors consider the numerical integration of stochastic differential delay equations


with initial data x(t)=ψ(t),t[-τ,0]· Here τ(t)0,-τ:=inf{t-τ(t):t0}, x is a d-dimensional vector, w(t) is an m-dimensional Wiener process. For the equation, they introduce a new Euler method and prove its convergence in the mean-square sense. Further, the exponential mean-square stability of the proposed method is investigated.

65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations
60H10Stochastic ordinary differential equations
65L20Stability and convergence of numerical methods for ODE
34K50Stochastic functional-differential equations
65L06Multistep, Runge-Kutta, and extrapolation methods