Markov renewal limit theorems
Author:
S. V. Degtyar’
Translated by:
O. I. Klesov
Journal:
Theor. Probability and Math. Statist. 76 (2008), 33-40
MSC (2000):
Primary 60K15, 60J25
DOI:
https://doi.org/10.1090/S0094-9000-08-00729-1
Published electronically:
July 10, 2008
Full-text PDF Free Access
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Additional Information
Abstract: We extend the fundamental results of the classical renewal theory to the so-called Markov renewal equation. We prove the Markov renewal theorems for the scheme of series.
References
- V. M. Shurenkov, Ergodic theorems and related problems, VSP, Utrecht, 1998. MR 1690361
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- N. Ya. Vilenkin, E. A. Gorin, A. G. Kostyuchenko, S. G. Krasnosel′skiĭ, S. G. Kreĭn, V. P. Maslov, B. S. Mityagin, Yu. I. Petunin, Ya. B. Rutitskii, V. I. Sobolev, V. Ya. Stetsenko, L. D. Faddeev, and E. S. Tsitlanadze, Functional analysis, Wolters-Noordhoff Publishing, Groningen, 1972. Translated from the Russian by Richard E. Flaherty; English edition edited by George F. Votruba with the collaboration of Leo F. Boron. MR 0390693
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- D. Alimov and V. M. Shurenkov, Markov renewal theorems in a scheme of series, Ukrain. Mat. Zh. 42 (1990), no. 11, 1443–1448 (Russian, with Ukrainian summary); English transl., Ukrainian Math. J. 42 (1990), no. 11, 1283–1288 (1991). MR 1098434, DOI https://doi.org/10.1007/BF01066181
References
- V. M. Shurenkov, Ergodic Theorems and Related Problems, “Nauka”, Moscow, 1989; English transl., VSP International Science Publishers, Utrecht, 1998. MR 1690361 (2000i:60002)
- T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–New York, 1966. MR 0203473 (34:3324)
- N. Ya. Vilenkin, E. A. Gorin, A. G. Kostyuchenko, S. G. Krasnosel$’$skiĭ, S. G. Kreĭn, V. P. Maslov, B. S. Mityagin, Yu. I. Petunin, Ya. B. Rutitskiĭ, V. I. Sobolev, A. Ya. Stetsenko, L. D. Faddeev, and E. S. Tsitlanadze, Functional Analysis, Second edition, “Nauka”, Moscow, 1964; English transl., Wolters-Noordhoff Publishing, Groningen, 1972. MR 0390693 (52:11516)
- N. V. Kartashov, Inequalities in stability and ergodicity theorems for Markov chains with a general phase space. I, Teor. Veroyatnost. i Primenen. 30 (1985), no. 2, 230–240; English transl. in Theory Probab. Appl. 30 (1985), no. 2, 507–515. MR 792617 (87c:60052a)
- D. Alimov and V. M. Shurenkov, Markov renewal theorems in a scheme of series, Ukrain. Mat. Zh. 42 (1990), no. 11, 1443–1448; English transl. in Ukrainian Math. J. 42 (1990), no. 11, 1283–1288. MR 1098434 (92g:60119)
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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
Keywords:
Markov renewal equation
Received by editor(s):
September 6, 2005
Published electronically:
July 10, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
