On Modified Crank–Nicholson Difference Schemes for Stochastic Parabolic Equation

Abstract We consider the modified Crank–Nicholson difference schemes for the approximate solution of the initial value Cauchy problem for stochastic parabolic equation in a Hilbert space H with the self-adjoint positive definite operator A. Here: (1) w t is a standard Wiener process given on the probability space (Ω,F,P). (2) f(t) is an element of space that consists of H 1-value processes for which the condition is satisfied. The estimate of convergence for the solution of these difference schemes is obtained. Keywords: ConvergenceDifference schemesStochastic parabolic equationAMS Subject Classification: 60H1560J35

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