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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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


Author: M. V. Kartashov
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
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

Abstract: 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
Email: winf@ln.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-08-00712-6
PII: S 0094-9000(08)00712-6
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