Date of Award

August 2015

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Bruce Wade

Second Advisor

Chao Zhu

Committee Members

Richard Stockbridge, Hans Volkmer, Wei Wei


Mean-Square Stability, Numerical Solution of Stochastic Differential Equations


This work proposes a novel weak Simpson method for numerical solution for a class of stochastic differential equations. We show that such a method has weak convergence of order one in general and weak convergence of order three under certain additional assumptions. This work also aims to determine the mean-square stability region of the weak Simpson method for linear stochastic differential equations with multiplicative noises. In this work, a mean-square stability region of the weak Simpson scheme is identified, and stepsizes for the numerical method where errors propagation are under control in well-defined sense are given. The main results are illustrated with numerical examples.

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