Limit theorems for difference additive functionals

Author:
Yu. M. Kartashov

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **83** (2010).

Journal:
Theor. Probability and Math. Statist. **83** (2011), 83-94

MSC (2010):
Primary 60J55, 60J45, 60F17

Published electronically:
February 2, 2012

MathSciNet review:
2768850

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider additive functionals defined on Markov chains that approximate a Markov process. Sufficient conditions are obtained for the convergence of the functionals. These conditions are expressed in terms of convergence of some conditional expectations (called the characteristics of the functionals) under general assumptions on the convergence of processes. Sufficient conditions for the uniform convergence of additive functionals are also given.

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Additional Information

**Yu. M. Kartashov**

Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Email:
kartashov-y@yandex.ru

DOI:
http://dx.doi.org/10.1090/S0094-9000-2012-00843-0

Keywords:
Additive functional,
characteristics of an additive functional,
invariance principle

Received by editor(s):
March 3, 2010

Published electronically:
February 2, 2012

Article copyright:
© Copyright 2012
American Mathematical Society