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

 

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
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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
PII: S 0094-9000(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