Strong Markov approximation of Lévy processes and their generalizations in a scheme of series
Author:
T. I. Kosenkova
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 86 (2013), 123-136
MSC (2010):
Primary 60J25, 60F17, 60B10
DOI:
https://doi.org/10.1090/S0094-9000-2013-00893-X
Published electronically:
August 20, 2013
MathSciNet review:
2986454
Full-text PDF Free Access
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Additional Information
Abstract: The notion of the strong Markov approximation that generalizes the notion of the Markov approximation is introduced. We consider an infinitesimal scheme of series that satisfies the assumptions of a Gnedenko theorem. Under these assumptions, we prove that a sequence of step processes constructed from a corresponding random walk is a strong Markov approximation for a Lévy process. The same result is obtained for a sequence of difference approximations of a solution to a stochastic differential equation driven by a Lévy noise.
References
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References
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- A. M. Kulik, Markov approximation of stable processes by random walks, Theory Stoch. Process. 12(28) (2006), no. 1–2, 87–93. MR 2316289 (2008j:60082)
- Yu. N. Kartashov and A. M. Kulik, Weak convergence of additive functionals of a sequence of Markov chains, Theory Stoch. Process. 15(31) (2009), no. 1, 15–32. MR 2603167 (2011a:60130)
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Additional Information
T. I. Kosenkova
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email:
tanya.kosenkova@gmail.com
Keywords:
Lévy processes,
central limit theorem in a scheme of series,
strong Markov approximation
Received by editor(s):
June 21, 2011
Published electronically:
August 20, 2013
Article copyright:
© Copyright 2013
American Mathematical Society
