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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Strong Markov approximation of Lévy processes and their generalizations in a scheme of series


Author: T. I. Kosenkova
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 123-136
MSC (2010): Primary 60J25, 60F17, 60B10
Published electronically: August 20, 2013
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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

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00893-X
PII: S 0094-9000(2013)00893-X
Keywords: L\'evy 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