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2014 Markov chain approximations for transition densities of Lévy processes
Aleksandar Mijatovic, Matija Vidmar, Saul Jacka
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Electron. J. Probab. 19: 1-37 (2014). DOI: 10.1214/EJP.v19-2208

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.

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Aleksandar Mijatovic. Matija Vidmar. Saul Jacka. "Markov chain approximations for transition densities of Lévy processes." Electron. J. Probab. 19 1 - 37, 2014. https://doi.org/10.1214/EJP.v19-2208

Information

Accepted: 13 January 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1303.60038
MathSciNet: MR3164760
Digital Object Identifier: 10.1214/EJP.v19-2208

Subjects:
Primary: 60G51

Keywords: continuous-time Markov chain , convergence rates for semi-groups and transition densities , Levy process , ‎spectral representation

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