On the Rate of Convergence of Weak Euler Approximation for Nondegenerate Itô Diffusion and Jump Processes

Abstract

The paper studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.

Cited by in corpus (2)

• On the Rate of Convergence of Weak Euler Approximation for Nondegenerate SDEs Driven by Levy Processes
• On the rate of convergence of weak Euler approximation for non-degenerate SDEs