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Numerical Solutions Of Stochastic Differential Equations, Liguo Wang

Doctoral Dissertations

In this dissertation, we consider the problem of simulation of stochastic differential equations driven by Brownian motions or the general Levy processes. There are two types of convergence for a numerical solution of a stochastic differential equation, the strong convergence and the weak convergence. We first introduce the strong convergence of the tamed Euler-Maruyama scheme under non-globally Lipschitz conditions, which allow the polynomial growth for the drift and diffusion coefficients. Then we prove a new weak convergence theorem given that the drift and diffusion coefficients of the stochastic differential equation are only twice continuously differentiable with bounded derivatives up to …