Overshoot functionals for almost semicontinuous processes defined on a Markov chain
Author:
E. V. Karnaukh
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 76 (2008), 49-57
MSC (2000):
Primary 60G50, 60J70; Secondary 60K10, 60K15
DOI:
https://doi.org/10.1090/S0094-9000-08-00731-X
Published electronically:
July 14, 2008
MathSciNet review:
2368739
Full-text PDF Free Access
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Additional Information
Abstract: The distributions of overshoot functionals are considered in the paper for almost semicontinuous processes defined on a finite irreducible Markov chain.
References
- D. V. Gusak, Granichnī zadachī dlya protsesīv z nezalezhnimi prirostami na skīnchennikh lantsyugakh Markova ta dlya napīvmarkovs′kikh protsesīv, Trudi Īnstitutu Matematiki Natsīonal′noï Akademīï Nauk Ukraïni [Proceedings of the Institute of Mathematics of the National Academy of Sciences of the Ukraine], vol. 18, Natsīonal′na Akademīya Nauk Ukraïni, Īnstitut Matematiki, Kiev, 1998 (Ukrainian, with English and Ukrainian summaries). MR 1710395
- Søren Asmussen, Ruin probabilities, Advanced Series on Statistical Science & Applied Probability, vol. 2, World Scientific Publishing Co., Inc., River Edge, NJ, 2000. MR 1794582
- D. V. Gusak, The distribution of extrema for risk processes on a finite Markov chain, Theory Stoch. Process. 7(23) (2001), no. 1–2, 109–120.
- D. V. Gusak and E. V. Karnaukh, Matrix factorization identity for almost semi-continuous processes on a Markov chain, Theory Stoch. Process. 11 (2005), no. 1-2, 40–47. MR 2327445
- V. S. Korolyuk and A. F. Turbin, Polumarkovskie protsessy i ikh prilozheniya, Izdat. “Naukova Dumka”, Kiev, 1976 (Russian). MR 0420902
References
- D. V. Gusak, Boundary Problems for Processes with Independent Increments on Finite Markov Chains and for Semi-Markov Processes, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, 1998. (Ukrainian) MR 1710395 (2000m:60050)
- S. Asmussen, Ruin Probabilities, World Scientific, Singapore, 2000. MR 1794582 (2001m:62119)
- D. V. Gusak, The distribution of extrema for risk processes on a finite Markov chain, Theory Stoch. Process. 7(23) (2001), no. 1–2, 109–120.
- D. V. Gusak and E. V. Karnaukh, Matrix factorization identity for almost semi-continuous processes on a Markov chain, Theory Stoch. Process. 11(27) (2005), no. 1–2, 40–47. MR 2327445 (2008e:60314)
- V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and their Applications, “Naukova dumka”, Kiev, 1976. (Russian) MR 0420902 (54:8913)
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Additional Information
E. V. Karnaukh
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
kveugene@univ.kiev.ua
Keywords:
Overshoot functionals,
almost semicontinuous processes,
ruin probability
Received by editor(s):
October 31, 2005
Published electronically:
July 14, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
