@article{EJP2208,
author = {Aleksandar Mijatovic and Matija Vidmar and Saul Jacka},
title = {Markov chain approximations for transition densities of Lévy processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Levy process, continuous-time Markov chain, spectral representation, convergence rates for semi-groups and transition densities},
abstract = {We consider the convergence of a continuous-time Markov chain approximation $X^h$, $h>0$, to an $\mathbb{R}^d$-valued Lévy process $X$. The state space of $X^h$ is an equidistant lattice and its $Q$-matrix is chosen to approximate the generator of $X$. In dimension one ($d=1$), and then under a general sufficient condition for the existence of transition densities of $X$, we establish sharp convergence rates of the normalised probability mass function of $X^h$ to the probability density function of $X$. In higher dimensions ($d>1$), rates of convergence are obtained under a technical condition, which is satisfied when the diffusion matrix is non-degenerate.},
pages = {no. 7, 1-37},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2208},
url = {http://ejp.ejpecp.org/article/view/2208}}