Approximation theorems for the solution of stochastic functional differential equations with discontinuous initial data
Faculty of Sciences. Mathematics and Computer Science
International journal of innovation in science and mathematics
, p. 273-279
University of Antwerp
Here Stochastic Functional Differential Equations(S.F.D.Es) 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.Es 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  to include S.F.D.Es with both drift and diffusion coefficients. The work on approximation in  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.