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Markov chain approximations for transition densities of Lévy processes
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Mijatović, Aleksandar, Vidmar, Matija and Jacka, Saul D. (2014) Markov chain approximations for transition densities of Lévy processes. Electronic Journal of Probability, Volume 19 . pp. 1-37. Article number 7. doi:10.1214/EJP.v19-2208 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/EJP.v19-2208
Abstract
We consider the convergence of a continuous-time Markov chain approximation Xh, h>0, to an Rd-valued Lévy process X. The state space of Xh 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 Xh 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes, Lévy processes | ||||
Journal or Publication Title: | Electronic Journal of Probability | ||||
Publisher: | University of Washington. Dept. of Mathematics | ||||
ISSN: | 1083-6489 | ||||
Official Date: | 13 January 2014 | ||||
Dates: |
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Volume: | Volume 19 | ||||
Page Range: | pp. 1-37 | ||||
Article Number: | Article number 7 | ||||
DOI: | 10.1214/EJP.v19-2208 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 26 December 2015 | ||||
Date of first compliant Open Access: | 26 December 2015 | ||||
Funder: | Javni Sklad Republike Slovenije za Razvoj Kadrov in Štipendije [Slovene Human Resources and Scholarship Fund] | ||||
Grant number: | 11010-543/2011 (JSRSRKS) |
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