Distributions of overshoots for almost continuous stochastic processes defined on a Markov chain
Author:
M. S. Gerych
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 94 (2017), 37-52
MSC (2010):
Primary 42C40; Secondary 60G12
DOI:
https://doi.org/10.1090/tpms/1007
Published electronically:
August 25, 2017
MathSciNet review:
3553452
Full-text PDF
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Additional Information
Abstract: We study the distributions of overshoots for the almost semi-continuous processes defined on a Markov chain. For these processes, we obtain the limit distributions of overshoots for the infinite and zero horizons.
References
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References
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- I. I. Ezhov and A. V. Skorohod, Markov processes which are homogeneous in the second component. I, Teor. Veroyatnost. Primenen. 14 (1969), no. 4, 679–692. English transl. in Theory Probab. Appl. 14 (1969), no. 4, 652–667. MR 0267640
- E. Arjas, On a fundamental identity in the theory of semi-Markov processes, Adv. Appl Probab. 4 (1972), no. 2, 258–270. MR 0339355
- A. A. Mogul’skĭ, Factorization identities for processes with independent increments, given on a finite Markov chain, Teor. Veroyatnost. Mat. Statist. 11 (1974), 86–96; English transl. in Theory Probab. Math. Statist. 11 (1974), 87–98.
- S. Asmussen and H. Albrecher, Ruin Probabilities, World Scientific, Hackensack, 2010. MR 2766220
- D. V. Gusak, Boundary Problems for Processes with Independent Increments Defined on Finite Markov Chains and for Semi-Markov Processes, Institute of Mathematics, National Academy of Science of Ukraine, Kyiv, 1998. (Ukrainian) MR 1710395
- E. V. Karnaukh, Boundary problems for a class of processes defined on a Markov chain, Abstract of thesis kand. fiz.-mat. nauk, Institute of Mathematics, National Academy of Science of Ukraine, Kyiv, 2007. (Ukrainian)
- V. I. Lotov and N. G. Orlova, Factorization representations in boundary value problems for random walks defined on a Markov chain, Sibirsk. Mat. Zh. 46 (2005), no. 4, 833–840; English transl. in Siberian Math. J. 46 (2005), no. 4, 661–667. MR 2169400
- D. V. Gusak and M. S. Gerych, On the moment-generating functions of extrema and their complements for almost semi-continuous integer-valued Poisson processes on Markov chains, Ukr. Mat. Zh. (2015) 67 no. 8, 1034–1049; English transl in Ukrainian Math. J. (2015) 67 no. 8, 1164–1182. MR 3473711
- D. V. Gusak and A. I. Tureniyazova, The distribution of some boundary functionals for lattice Poisson processes defined on a Markov chain, Asymptotic Methods in Studies of Stochastic Models, Institute of Mathematics, Academy of Science of Ukrainian SSR, Kiev, 1967, 21–27. (Russian) MR 943353
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- M. S. Gerych, A ramification of the main factorization identity for almost semi-continuous lattice Poisson processes defined on a Markov chain, Carpathian Math. Publ. 4 (2012), no. 2, 229–240. (Ukrainian)
- M. S. Gerych, Generating functions of extremums and their complements for semi-continuous from above lattice Poisson processes defined on a Markov chain, Visn. Kyiv Shevchenko Nat. Univ. Ser. Fiz.–Mat. 1 (2013), 21–27. (Ukrainian)
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Additional Information
M. S. Gerych
Affiliation:
Department of Probability Theory and Mathematical Analysis, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod 88000, Ukraine
Email:
miroslava.gerich@yandex.ua
Keywords:
Almost semi-continuous process defined on a Markov chain,
overshoot functionals,
distributions of overshoots for the infinite and zero horizons
Received by editor(s):
February 12, 2016
Published electronically:
August 25, 2017
Article copyright:
© Copyright 2017
American Mathematical Society
