Karhunen-Loéve expansion of Brownian motion for approximate solutions of linear stochastic differential models using Picard iteration

O.P. Ogundile, S.O. Edeki

Abstract


This work presents an application of the Picard Iterative Method (PIM) to a class of Stochastic Differential Equations where the randomness in the equation is considered in terms of the Karhunen-Loéve Expansion finite series. Two applicable numerical examples are considered to illustrate the convergence of the approximate solutions to the exact solutions and also to check the efficiency of the method. The results obtained show clearly that accuracy will be more visible by increasing the number of terms in the iteration. Thus, it is recommended for nonlinear financial models of different classes of Stochastic Differential Equations.

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Published: 2020-07-09

How to Cite this Article:

O.P. Ogundile, S.O. Edeki, Karhunen-Loéve expansion of Brownian motion for approximate solutions of linear stochastic differential models using Picard iteration, J. Math. Comput. Sci., 10 (2020), 1712-1723

Copyright © 2020 O.P. Ogundile, S.O. Edeki. 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.

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