Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 69-75
doi:10.1155/S1048953395000062

Extension of the method of quasilinearization for stochastic initial value problems

N. Shahzad1,3 and Farzana A. McRae2

1Florida Institute of Technology, Department of Applied Mathematics, Melbourne 32901, Florida, USA
2Jacksonville University, Department of Mathematics, Jacksonville 32211, Florida, USA
3Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Received 1 August 1994; Revised 1 November 1994

Copyright © 1995 N. Shahzad and Farzana A. McRae. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we extend the method of quasilinearization to stochastic initial value problems. Further we prove that the iterates converge uniformly almost surely to the unique solution and the convergence is quadratic.