On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes - Open Access Library Journal

OALibJ > Vol.3 No.1, January 2016

On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes ()

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DOI: 10.4236/oalib.1102247 1,841 Downloads 4,878 Views Citations

Author(s)

Sunday Jacob Kayode¹, Akeem Adebayo Ganiyu², Adegoke Sule Ajiboye³

Affiliation(s)

¹Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
²Mathematics Department, Adeyemi College of Education, Ondo, Nigeria.
³Department of Statistics, Federal University of Technology, Akure, Nigeria.

ABSTRACT

In this work, a one-step method of Euler-Maruyama (EMM) type has been developed for the solution of general first order stochastic differential equations (SDEs) using Ito integral equation as basis tool. The effect of varying stepsizes on the numerical solution is also examined for the SDEs. Two problems of first order SDEs are solved. Absolute errors for the problems are obtained from which the mean absolute errors (MAEs) are calculated. Comparison of variation in stepsizes is achieved using the MAEs. The results show that the MAEs decrease as the stepsize decreases. The strong orders of convergence and the residuals for the problem for the theoretical are respectively obtained using Least Square Fit. This work produces numerical values for the solution to the problems which differ from the existing methods of EMM type in which results are always obtained by simulation.

KEYWORDS

One-Step Method, Ito Integral, Stochastic State Model, Gaussian White Noise, Wiener Process, Wiener Increment

Share and Cite:

Kayode, S. , Ganiyu, A. and Ajiboye, A. (2016) On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes. Open Access Library Journal, 3, 1-15. doi: 10.4236/oalib.1102247.

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