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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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.

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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