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The ergodicity and stability of quasi-homogeneous Markov semigroups of operators
Author(s):
M.
V.
Kartashov
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
59-68.
MSC (2000):
Primary 60J45;
Secondary 60A05
Posted:
August 18, 2006
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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.
References:
-
- 1.
- N. V. Kartashov, Strong Stable Markov Chains, VSP/``TBiMC'', Utrecht, The Netherlands/Kyiv, Ukraine, 1996. MR 1451375 (99e:60150)
- 2.
- E. B. Dynkin, Theory of Markov Processes, ``Fizmatlit'', Moscow, 1962; English transl., Prentice-Hall, Inc., Englewood Cliffs, NJ, 1961. MR 0131900 (24:A1747)
- 3.
- I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, vol. 2, ``Nauka'', Moscow, 1973; English transl., Springer-Verlag, Berlin, 2004. MR 2058260 (2005a:60003)
- 4.
- T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966. MR 0203473 (34:3324)
- 5.
- N. V. Kartashov, On the stability of almost time-homogeneous Markov semigroups of operators, Teor. Imovirnost. Matem. Statist. 71 (2004), 105-113; English transl. in Theory Probab. Math. Statist. 71 (2005), 119-128. MR 2144325 (2006b:60172)
- 6.
- D. Revuz, Markov Chains, North-Holland Elsevier, Amsterdam, 1975. MR 0415773 (54:3852)
- 7.
- O. Hernandez-Lerma and J. B. Lasser, Markov Chains and Invariant Probabilities, Birkhäuser Verlag, Basel-Boston-Berlin, 2003. MR 1974383 (2004b:60002)
- 8.
- N. V. Kartashov, Uniformly ergodic jump Markov processes with bounded intensities, Teor. Imovirnost. Matem. Statist. 52 (1995), 86-98; English transl. in Theory Probab. Math. Statist. 52 (1995), 86-98. MR 1445541 (97m:60104)
- 9.
- -, Computation and estimation of the exponential ergodicity exponent for general Markov processes and chains with recurrent kernels, Teor. Imovirnost. Matem. Statist. 54 (1996), 47-57; English transl. in Theory Probab. Math. Statist. 54 (1997), 49-60. MR 1644643 (99e:60199)
- 10.
- K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000. MR 1721989 (2000i:47075)
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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
Email:
winf@ln.ua
DOI:
10.1090/S0094-9000-06-00664-8
PII:
S 0094-9000(06)00664-8
Keywords:
A semigroup of operators,
infinitesimal operator,
uniform ergodicity,
uniform stability
Received by editor(s):
29/SEP/2004
Posted:
August 18, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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