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Finite-difference approximation for the solution of a stochastic evolution equation. (Russian) Zbl 0619.65149
An explicit finite-difference scheme for a stochastic evolution differential equation in a Hilbert space with monotone coefficients is considered. A similar scheme for equations with Lipschitz coefficients was considered by M. A. Karabash [ibid. 8, 74-78 (1980; Zbl 0442.49019)]. An implicit finite-difference scheme for monotone stochastic evolution equations in a Banach space with diffusion coefficient, not depending on the phase variable, was constructed by A. Bensoussan and R. Temam [Isr. J. Math. 11, 95-129 (1972; Zbl 0241.35009)].
65C99 Probabilistic methods, stochastic differential equations
65R20 Numerical methods for integral equations
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
60H20 Stochastic integral equations
45N05 Abstract integral equations, integral equations in abstract spaces