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One linear analytic approximation for stochastic integrodifferential equations. (English) Zbl 1240.60153

Summary: This article concerns the construction of approximate solutions for a general stochastic integro-differential equation which is not explicitly solvable and whose coefficients depend functionally on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the \(L^p\)-th norm, uniformly on the time interval. The convergence with probability one is also given.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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