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Sufficient conditions for the convergence of local-time type functionals of Markov approximations
Author(s):
Yu.
M.
Kartashov
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 77
(2007).
Journal:
Theor. Probability and Math. Statist.
No. 77
(2008),
39-55.
MSC (2000):
Primary 60J55, 60J45, 60F17
Posted:
January 14, 2009
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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 local-time type functionals of random walks approaching an  -stable process with index  .
References:
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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:
10.1090/S0094-9000-09-00746-7
PII:
S 0094-9000(09)00746-7
Keywords:
Additive functional,
characteristic of an additive functional,
Markov approximation
Received by editor(s):
17/MAY/2007
Posted:
January 14, 2009
Additional Notes:
The work is supported by the Ministry of Science and Education of Ukraine, Project N GP/F13/0095
Copyright of article:
Copyright
2009,
American Mathematical Society
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