Runge-Kutta and recursive distribution numerical methods for approximate solution of stochastic differential equations

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Title: Runge-Kutta and recursive distribution numerical methods for approximate solution of stochastic differential equations
Author: Abukhaled, Marwan Ibrahim
Abstract: This research concerns numerical solution of stochastic differential equations and is divided into two different and independent approaches . In the first approach , a class of Runge -Kutta methods is developed , analyzed and numerically tested . It is shown that these methods are of second -order accuracy in the weak sense for estimating expectations of functions of the solution for scalar as well as for systems of stochastic differential equations . It is also shown that in these methods , variance reduction techniques can be applied to reduce the stochastic error involved in estimating the expectations of functions of the solution . These second -order explicit methods are unique in the sense that they do not involve derivatives of the drift and diffusion coefficients and they can be easily programmed and implemented . In the second approach , it is shown that probability distributions of approximate sample paths of the solution satisfy a recursive integral equation . These probability distributions can then be approximated by numerically solving the integral equation . The advantage of this approach is the avoidance of computing thousands of sample paths as is generally the case in most standard numerical methods . This approach is shown to be useful for numerical solution of first -passage time problems .
URI: http : / /hdl .handle .net /2346 /10469
Date: 1995-05

Citation

Abukhaled, Marwan Ibrahim Runge-Kutta and recursive distribution numerical methods for approximate solution of stochastic differential equations. Doctoral dissertation, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /10469 .

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