Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Distributions of overshoots for almost continuous stochastic processes defined on a Markov chain
M. S. Gerych
Download PDF
Abstract: In this paper we study the distributions of overshoots for the almost semi-continuous processes defined on a Markov chain. For these processes, we get the limit distributions of overshoots over the infinitely far and zero levels.
Keywords: almost semi-continuous process defined on Markov chain, overshoots functionals ,distributions of overshoots over the infinitely far and zero levels
Bibliography: 1. Ezhov I.I., Skorokhod A.V. Markov processes, homogeneous by second component // Probability teor. and its appl. – 1969. – 14, № 1. – P. 3-14, № 4 – P. 679-692.
2. Arjas E. On a fundamental identity in the theory of semi-Markov processes // Advances in Applied Probability. – 1972. Vol. 4, № 2, P. 258-270.
3. Asmussen S., Albrecher H. Ruin Probabilities. – Hackensack: World Scientific Publishing Company,2010. – p. 621.
4. Husak D.V. Boundary problems for processes with independent increments on finite Markov chain and for semi-Markov processes. – Kiev: Institute of Mathematics NAN Ukrain, 1998. – p. 320.
5. Karnaukh Ye.V. Boundary value problems for one class processes on Markov chain: Thesis abstract of PhD Ph.-mat. sc. – Kiev, 2007, – p. 18.
6. Lotov V.I., Orlova N.G. Factorization Representations in the Boundary Crossing Problems for Random Walks on a Markov Chain// Sib. Math. Journal. – 2005. – T. 46, № 4. – P. 833-840.
7. Herych, M.S., Husak(Gusak) D.V.On the Moment-Generating Functions of Extrema and Their Complements for Almost Semicontinuous Integer-Valued Poisson Processes on Markov Chains //Ukr. Math. Jorn.,– 2015. – Vol. 67, № 8, P. 1034–1049.
8. Husak D.V., Tureniyazova A.I. Distribution of some boundary functionals for lattice Poisson processes on Markov chain// Asymptotic methods in stochastic models study: Col.sc.p.– Institute of Mathematics NAN Ukrain, – 1967.– P. 21-27.
9. Husak D.V. Processes with stationary independent increments in the Risk theory. – Kiev: Institute of Mathematics NAN Ukrain, 2011. – p. 544.
10. Herych M. S. Refinements of basic faktorizational identity for almost semi-continuous lattice processes on Markov chain// Carpathian mathematical publish papers. – 2012. – Vol. 4, №2. – P.229-240.
11. Herych M. S. Moment generating functions of extremums and their complemets for upper semi-continuous lattice Poison process on Markov chain// Bulletin of Taras Shevchenko National University of Kyiv Series Physics- Mathematics . – 2013. – №1. – P. 21-27.
