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Theory of Probability and Mathematical Statistics

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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
Published electronically: January 14, 2009
MathSciNet review: 2432771
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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 $ 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\leq1$.

References [Enhancements On Off] (What's this?)

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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

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