Sufficient conditions for the convergence of local-time type functionals of Markov approximations
Author:
Yu. M. Kartashov
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 77 (2008), 39-55
MSC (2000):
Primary 60J55, 60J45, 60F17
DOI:
https://doi.org/10.1090/S0094-9000-09-00746-7
Published electronically:
January 14, 2009
MathSciNet review:
2432771
Full-text PDF Free Access
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Abstract: A sufficient condition is obtained for the weak convergence of additive functionals defined on a sequence of Markov chains $X_n$ approaching a Markov process $X$. The condition is expressed in terms of transient probabilities of the chains $X_n$. An application of the main result is given for the convergence on the Cantor set of local-time type functionals of random walks approaching an $\alpha$-stable process with index $\alpha \leq 1$.
References
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References
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- A. M. Kulik and Yu. N. Kartashov, Invariance principle for additive functionals of Markov chains, arXiv:0704.0508v1.
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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:
kartashov-y@yandex.ru
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
