The moments of the artificial regeneration for an asymptotically degenerate family of Markov functionals
Author:
S. V. Degtyar’
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 75 (2007), 1-8
MSC (2000):
Primary 60K15, 60J25
DOI:
https://doi.org/10.1090/S0094-9000-07-00709-0
Published electronically:
January 23, 2008
MathSciNet review:
2321176
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
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
- V. M. Shurenkov, Ergodic theorems and related problems, VSP, Utrecht, 1998. MR 1690361
- N. I. Portenko, A. V. Skorokhod, and V. M. Shurenkov, Markov processes, Current problems in mathematics. Fundamental directions, Vol. 46 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, pp. 5–245 (Russian). MR 1039619
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- I. N. Kovalenko, Limit theorems of reliability theory, Kibernetika (Kiev) 6 (1977), 106–116, 152 (Russian, with English summary). MR 518465
- E. Nummelin, Uniform and ratio limit theorems for Markov renewal and semi-regenerative processes on a general state space, Ann. Inst. H. Poincaré Sect. B (N.S.) 14 (1978), no. 2, 119–143 (English, with French summary). MR 507729
- K. B. Athreya, D. McDonald, and P. Ney, Limit theorems for semi-Markov processes and renewal theory for Markov chains, Ann. Probab. 6 (1978), no. 5, 788–797. MR 503952
References
- V. M. Shurenkov, Ergodic Theorems and Related Problems, Moscow, “Nauka”, 1989; English transl., VSP International Science Publishers, Leiden, 1998. MR 1690361 (2000i:60002)
- 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)
- T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–New York, 1966. MR 0203473 (34:3324)
- I. N. Kovalenko, Limit theorems of reliability theory, Kibernetika 6 (1977), 106–116. (Russian) MR 0518465 (58:24589)
- 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)
- K. B. Athreya, D. McDonald, and P. Ney, Limit theorems for semi-Markov processes and renewal theory for Markov chains, Ann. Probab. (1978), no. 6, 788–797. MR 503952 (80f:60076)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2000):
60K15,
60J25
Retrieve articles in all journals
with MSC (2000):
60K15,
60J25
Additional Information
S. V. Degtyar’
Affiliation:
Department of Higher Mathematics, Vadym Hetman Kyiv National Economic University, Peremogy Avenue 54/1, Kyiv 03057, Ukraine
Keywords:
Markov functionals,
homogeneous ergodic processes
Received by editor(s):
September 6, 2005
Published electronically:
January 23, 2008
Article copyright:
© Copyright 2007
American Mathematical Society