Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 69-75
Extension of the method of quasilinearization for stochastic
initial value problems
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.
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.