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Theory of Probability and Mathematical Statistics

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Convergence of a sequence of Markov chains to a diffusion type process


Authors: G. L. Kulinich and A. V. Yershov
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 115-131
MSC (2000): Primary 60H10; Secondary 34G10, 47A50, 47D06
DOI: https://doi.org/10.1090/S0094-9000-09-00766-2
Published electronically: August 4, 2009
MathSciNet review: 2446853
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Abstract | References | Similar Articles | Additional Information

Abstract: A random polygonal line constructed from a sequence of series of homogeneous Markov chains is considered under rather nonregular dependence of their local characteristics on a series number. Sufficient conditions are obtained for the weak convergence of a random polygonal line to a diffusion type process. The conditions are expressed explicitly in terms of local characteristics of the Markov chains.


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Additional Information

G. L. Kulinich
Affiliation: Department of General Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: a_yershov@univ.kiev.ua

A. V. Yershov
Affiliation: Department of General Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-09-00766-2
Keywords: A sequence of series of Markov chains, nonregular dependence of local characteristics of Markov chains on the number of a series, a random polygonal line, weak convergence, stochastic differential equation, diffusion type processes
Received by editor(s): May 7, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society