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An essay on Gnedenko's theorem


Author: A. Yu. Veretennikov
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 17-25
MSC (2000): Primary 60J10, 60F05
DOI: https://doi.org/10.1090/S0094-9000-05-00610-1
Published electronically: February 7, 2005
MathSciNet review: 2110901
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Abstract | References | Similar Articles | Additional Information

Abstract: A local central limit theorem is established for a Markov chain on a lattice under recurrence type assumptions and a simple additional assumption on conditional distributions of the process. The main result extends, in particular, the classical theorem by B. V. Gnedenko for the case of independent identically distributed random variables (1948). Sufficient conditions for recurrence assumptions are provided.


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Additional Information

A. Yu. Veretennikov
Affiliation: Institute of Information Transmission Problems, 19 B. Karetnyi, Moscow 101447, Russia
Address at time of publication: School of Mathematics, University of Leeds, Woodhouse Lane, LS2 9JT, Leeds, UK
Email: veretenn@maths.leeds.ac.uk

DOI: https://doi.org/10.1090/S0094-9000-05-00610-1
Received by editor(s): April 4, 2002
Published electronically: February 7, 2005
Additional Notes: The work was supported by the grants INTAS-99-0590, EPSRC-GR/R40746/01, NFGRF 2301863, and RFBR-00-01-22000.
Article copyright: © Copyright 2005 American Mathematical Society

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