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Integral approximation of stochastic differential equations with anticipating initial conditions

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Abstract

We give a sequence of stochastic integro-differential equations that approximates a stochastic differential equation with an anticipating initial condition and localized Skorokhod stochastic integral. A sequence of solutions of these equations is obtained. The convergence of this sequence to a certain process implies that this process is a solution (generally speaking, local) of the original equation.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. M. Kulik

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  1. A. M. Kulik
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 7, pp. 936–945, July, 1995.

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Kulik, A.M. Integral approximation of stochastic differential equations with anticipating initial conditions. Ukr Math J 47, 1074–1084 (1995). https://doi.org/10.1007/BF01084903

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  • DOI: https://doi.org/10.1007/BF01084903

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