Precise estimates for the solution of stochastic functional differential equations with discontinuous initial data : part 1Precise estimates for the solution of stochastic functional differential equations with discontinuous initial data : part 1
Faculty of Sciences. Mathematics and Computer Science
Analytical and topological structures
International journal of innovative science, engineering & technology
1(2014):8, p. 179-191
University of Antwerp
In this work we have used the same introduction,notations and denitions as in . 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 Dierential 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 (, Theorem 10.2.2) to S.F.D.E.'s with discontinuous initial data. We have calculated this uniform error bound by computing the dierence between the actual solution process and it's Euler approximation and we have found the upper bound for this dierence. We have also discussed the dependence of this dierence 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 seechapters9and10.