Analytical problems of the asymptotic behavior of Markov functionals. II
Author:
S. V. Degtyar’
Translated by:
O. I. Klesov
Journal:
Theor. Probability and Math. Statist. 78 (2009), 15-21
MSC (2000):
Primary 60K15; Secondary 60J25
DOI:
https://doi.org/10.1090/S0094-9000-09-00758-3
Published electronically:
August 4, 2009
MathSciNet review:
2446845
Full-text PDF Free Access
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Abstract: The asymptotic behavior of Markov functionals of a homogeneous ergodic Markov process is studied in this paper.
References
- S. V. Degtyar′, Analytic problems of the asymptotics of Markov functionals. I, Teor. Ĭmovīr. Mat. Stat. 77 (2007), 28–35 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 77 (2008), 31–38. MR 2432770, DOI https://doi.org/10.1090/S0094-9000-09-00745-5
- 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
References
- S. V. Degtyar’, Analytical problems of the asymptotic behavior of Markov functionals. I, Teor. Imovir. Matem. Statist. 77 (2007), 28–35; English transl. in Theory Probab. Math. Statist. 77 (2008), 31–38. MR 2432770
- V. M. Shurenkov, Ergodic Theorems and Related Problems, Nauka, Moscow, 1989; English transl., VSP International Science Publishers, Leiden, 1998. MR 1690361 (2000i:60002)
- N. I. Portenko, A. S. Skorokhod, and V. M. Shurenkov, Markov Processes, Progress in Science and Technology. Current Problems in Mathematics. Fundamental Directions, vol. 46, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Akad. Nauk SSSR, Moscow, 1989. (Russian) MR 1039619 (91j:60113b)
- T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–New York, 1966. MR 0203473 (34:3324)
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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
Email:
sdegtyar@zra.kiev.ua
Keywords:
Markov functionals,
homogeneous ergodic process
Received by editor(s):
May 6, 2005
Published electronically:
August 4, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
