Sufficient conditions for the convergence of localtime type functionals of Markov approximations
Author:
Yu. M. Kartashov
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal:
Theor. Probability and Math. Statist. 77 (2008), 3955
MSC (2000):
Primary 60J55, 60J45, 60F17
Published electronically:
January 14, 2009
MathSciNet review:
2432771
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: A sufficient condition is obtained for the weak convergence of additive functionals defined on a sequence of Markov chains approaching a Markov process . The condition is expressed in terms of transient probabilities of the chains . An application of the main result is given for the convergence on the Cantor set of localtime type functionals of random walks approaching an stable process with index .
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Additional Information
Yu. M. Kartashov
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
kartashovy@yandex.ru
DOI:
http://dx.doi.org/10.1090/S0094900009007467
PII:
S 00949000(09)007467
Keywords:
Additive functional,
characteristic of an additive functional,
Markov approximation
Received by editor(s):
May 17, 2007
Published electronically:
January 14, 2009
Additional Notes:
The work is supported by the Ministry of Science and Education of Ukraine, Project N GP/F13/0095
Article copyright:
© Copyright 2009
American Mathematical Society
