Numerical solution of stochastic differential equation corresponding to continuous distributions
Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 709-720
Printed December 1, 2011
Mohammad Amini, Ali Reza Soheili, and Mahdi Allahdadi
Ferdowsi University of Mashhad, Ferdowsi University of Mashhad, University of Sistan and Baluchestan
Abstract : We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.
Keywords : stochastic differential equation, continuous distribution function, confidence interval, Euler-Maruyama method
MSC numbers : Primary 65C20; Secondary 65C10, 65C30
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