University of Khartoum

Precise Estimates for The Solution of Stochastic Functional Differential Equations With Discontinuous Initial Data (Part 1)

Precise Estimates for The Solution of Stochastic Functional Differential Equations With Discontinuous Initial Data (Part 1)

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Title: Precise Estimates for The Solution of Stochastic Functional Differential Equations With Discontinuous Initial Data (Part 1)
Author: Ahmed, Tagelsir A.; Van Casteren, Jan A.
Abstract: In this work we have used the same introduction,notations and de nitions as in [2]. Here we have proved a theorem in which we have established a uni- form error bound for the Euler approximation to the solution process of the Stochastic Funtional Di erential Equation (S.F.D.E.) (1.11) over the whole time interval [0; a]. This Theorem is an extension of the work of Kloeden and Platen ([6], Theorem 10.2.2) to S.F.D.E.'s with discontinuous initial data. We have calculated this uniform error bound by computing the di erence between the actual solution process and it's Euler approximation and we have found the upper bound for this di erence. We have also discussed the dependence of this di erence on the inital data.We have also proved that the Euler approx- imation of the solution process has the order of strong convergence = 0:5 see[6]chapters9and10. IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 1 Issue 8, October 2014. www.ijiset.com ISSN 2348 – 7968 179
URI: http://khartoumspace.uofk.edu/123456789/24759


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