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Theory of Probability and Mathematical Statistics

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The stability of transient quasi-homogeneous Markov semigroups and an estimate of the ruin probability

Author: M. V. Kartashov
Translated by: S. Kvasko
Journal: Theor. Probability and Math. Statist. 75 (2007), 41-50
MSC (2000): Primary 60J45; Secondary 60A05
Published electronically: January 23, 2008
MathSciNet review: 2321179
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Abstract | References | Similar Articles | Additional Information


A time nonhomogeneous semigroup of Markov operators in a Banach space is called quasi-homogeneous if its infinitesimal operator has a dense domain and can be represented as the sum of the infinitesimal operator of a homogeneous semigroup and a bounded operator function.

We obtain estimates of the strong stability of a nonhomogeneous semigroup for the case where the underlying homogeneous semigroup is uniformly transient.

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Additional Information

M. V. 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: Semigroup of operators, infinitesimal operator, uniform transiency, strong stability
Received by editor(s): December 19, 2005
Published electronically: January 23, 2008
Article copyright: © Copyright 2008 American Mathematical Society