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Higher-order implicit strong numerical schemes for stochastic differential equations. (English) Zbl 0925.65261
Summary: Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.
MSC:
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
60H10Stochastic ordinary differential equations
65L06Multistep, Runge-Kutta, and extrapolation methods
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