APPROXIMATE ANALYTICAL SOLUTIONS OF LINEAR STOCHASTIC DIFFERENTIAL MODELS BASED ON KARHUNEN-LOÉVE EXPANSION WITH FINITE SERIES TERMS

Ogundile, O. P. and Edeki, S.O. (2020) APPROXIMATE ANALYTICAL SOLUTIONS OF LINEAR STOCHASTIC DIFFERENTIAL MODELS BASED ON KARHUNEN-LOÉVE EXPANSION WITH FINITE SERIES TERMS. Commun. Math. Biol. Neurosci., 20. ISSN 2052-2541

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Abstract

Copyright © 2020 the author(s). 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: Stochastic Differential Equations (SDEs) as particular forms of Differential Equations (DEs) play immense roles in modeling of various phenomena with applications in physical sciences, and finance- such as stock option practices due to thermal and random fluctuations. The solutions of these SDEs, if they exist, are difficult to obtain, unlike those of the Differential Equations. In this paper, the white noise terms of the linear SDEs in Stratonovich forms are considered on the basis of Karhunen-Loéve Expansion finite series while Daftardar-Jafari Integral Method is proposed for approximate analytical solution of the linear Stratonovich Stochastic Differential Equations. Three numerical examples are considered to test the accuracy and effectiveness of this proposed method. The results obtained show clearly that the approximate solutions converge faster to the exact solutions even with fewer terms; though, higher terms increase the accuracy. The method is direct in terms of application. Thus, it is recommended for nonlinear financial models such as Ito Stochastic Differential Equations.

Item Type:	Article
Uncontrolled Keywords:	Stratonovich SDEs; population dynamics; Karhunen-Loéve expansion; approximate solution; differential models; option pricing; Daftardar-Jafari method.
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Mrs Patricia Nwokealisi
Date Deposited:	02 Jun 2022 10:57
Last Modified:	02 Jun 2022 10:57
URI:	http://eprints.covenantuniversity.edu.ng/id/eprint/15930

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