On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes
Probability
2014-01-13 v4 Analysis of PDEs
Abstract
The paper studies the rate of convergence of the weak Euler approximation for It\^{o} diffusion and jump processes with H\"{o}lder-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 H\"{o}lder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.
Keywords
Cite
@article{arxiv.1007.2914,
title = {On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes},
author = {Remigijus Mikulevičius and Changyong Zhang},
journal= {arXiv preprint arXiv:1007.2914},
year = {2014}
}