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The moments of the artificial regeneration for an asymptotically degenerate family of Markov functionals
Author(s):
S.
V.
Degtyar'
Translated by:
N. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
1-8.
MSC (2000):
Primary 60K15, 60J25
Posted:
January 23, 2008
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Additional information
Abstract:
We construct moments of the artificial regeneration satisfying certain conditions for a homogeneous ergodic Markov process related to a Markov functional in the scheme of series.
References:
-
- 1.
- V. M. Shurenkov, Ergodic Theorems and Related Problems, Moscow, ``Nauka'', 1989; English transl., VSP International Science Publishers, Leiden, 1998. MR 1690361 (2000i:60002)
- 2.
- N. I. Portenko, A. V. Skorokhod, and V. M. Shurenkov, Markov processes, Itogi Nauki i Tekhniki, Current problems in mathematics. Fundamental directions, vol. 46, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, pp. 5-245. (Russian) MR 1039619 (91j:60113b)
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- T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-New York, 1966. MR 0203473 (34:3324)
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- I. N. Kovalenko, Limit theorems of reliability theory, Kibernetika 6 (1977), 106-116. (Russian) MR 0518465 (58:24589)
- 5.
- E. Nummelin, Uniform and Ratio Limit Theorems for Markov Renewal and Semi-Regenerative Processes on a General State Space, Report Helsinki Univ. Technol. Inst. Math. Espoo, vol. A 98, 1977. MR 507729 (80a:60114)
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Additional Information:
S.
V.
Degtyar'
Affiliation:
Department of Higher Mathematics, Vadym Hetman Kyiv National Economic University, Peremogy Avenue 54/1, Kyiv 03057, Ukraine
DOI:
10.1090/S0094-9000-07-00709-0
PII:
S 0094-9000(07)00709-0
Keywords:
Markov functionals,
homogeneous ergodic processes
Received by editor(s):
6/SEP/2005
Posted:
January 23, 2008
Copyright of article:
Copyright
2007,
American Mathematical Society
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