Title
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
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
International journal of innovative science, engineering & technology
Volume/pages
1(2014) :8 , p. 179-191
ISSN
2348-7968
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
In this work we have used the same introduction,notations and denitions 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 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 ([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 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 see[6]chapters9and10.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/3ae846/10723.pdf
Handle