An essay on Gnedenko’s theorem

Veretennikov, A.

doi:10.1090/S0094-9000-05-00610-1

An essay on Gnedenko’s theorem

Author: A. Yu. Veretennikov
Translated by: The author
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: 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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