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Theory of Probability and Mathematical Statistics

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The ergodicity and stability of quasi-homogeneous Markov semigroups of operators

Author: M. V. Kartashov
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 59-68
MSC (2000): Primary 60J45; Secondary 60A05
Published electronically: August 18, 2006
MathSciNet review: 2168136
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Abstract: A nonhomogeneous-in-time semigroup of Markov operators acting in a Banach space is called quasi-homogeneous if the domain of its infinitesimal operator is dense and the operator itself can be represented as the sum of the infinitesimal operator of a homogeneous semigroup and a bounded operator function.

Under the condition that the basic homogeneous semigroup is uniformly ergodic, we prove the uniform ergodicity and strong stability of the nonhomogeneous semigroup and obtain the estimates of the rate of convergence in the corresponding limit theorems.

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Additional Information

M. V. Kartashov
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Keywords: A semigroup of operators, infinitesimal operator, uniform ergodicity, uniform stability
Received by editor(s): September 29, 2004
Published electronically: August 18, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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