TITLE:
On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes
AUTHORS:
Sunday Jacob Kayode, Akeem Adebayo Ganiyu, Adegoke Sule Ajiboye
KEYWORDS:
One-Step Method, Ito Integral, Stochastic State Model, Gaussian White Noise, Wiener Process, Wiener Increment
JOURNAL NAME:
Open Access Library Journal,
Vol.3 No.1,
January
29,
2016
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.