Approximation Theorems for The Solution of Stochastic Functional Differential Equations with Discontinuous Initial Data

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Year:
2014
Type of Publication:
Article
Keywords:
Approximation, Delay, Differential, Equation, Functional, Ordinary, Stochastic
Authors:
Tagelsir A Ahmed; J. A. Van Casteren
Journal:
IJISM
Volume:
2
Number:
2
Pages:
273-279
Month:
March
Abstract:
Here “Stochastic Functional Differential Equations(S.F.D.E’s)” means “Delay Stochastic Differential Equations”. In this work we have developed an Euler approximation scheme for the solution process of Stochastic Functional Differential Equation with possibly discontinuous initial data, and we have shown that this Euler scheme (under appropriate conditions) converges to the solution process as the mesh of the partition goes to zero. The approximation theorem which we have established gives us a method for approximating the solution of S.F.D.E’s with possibly discontinuous initial data. Note that here we are considering S.F.D.E which includes both drift and diffusion coefficients. The present work on approximation is an extension of the work on approximation in [1] to include S.F.D.E’s with both drift and diffusion coefficients. The work on approximation in [1] was suggested by Prof. Salah-E.A.Mohammed and it was done by Tagelsir A. Ahmed under the supervision of Prof. Salah-E.A.Mohammed.

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