In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model the spread options.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Luo, Yi, "Numerical Solutions for Stochastic Differential Equations and Some Examples" (2009). All Theses and Dissertations. 1762.
mathematics, stochastic differential equations, numerical solutions, Brownian motion