Sufficient conditions for the convergence of local-time 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), 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

Abstract | References | Similar Articles | 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 local-time 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:
kartashov-y@yandex.ru

DOI:
https://doi.org/10.1090/S0094-9000-09-00746-7

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