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On the limiting behaviour of a basic stochastic process

Published online by Cambridge University Press:  14 July 2016

İzzet Şahin  and
Oussama Achou
İzzet Şahin
Affiliation:
University of Ottawa
Oussama Achou
Affiliation:
University of Ottawa
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Abstract

Determination of the limiting distributions for a class of mixed-type stochastic processes with state-dependent rates of decline is reduced to the solution of a class of integral equations. For the case where the rate of decline is proportional to the state, some results are obtained by solving the integral equation of the process through Fuchs' method.

Keywords

MIXED TYPE STOCHASTIC PROCESSNON-MARKOVIAN PROCESSPROCESS WITH STATE DEPENDENT OUTPUT RATESTORAGE SYSTEMSPARTICLE COUNTERSQUEUINGINTEGRAL EQUATIONSFUCHS' METHODSECONDARY PROCESS

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 202 - 207
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Gaver, D. P. Jr. and Miller, R. G. Jr. (1962) Limiting distributions for some storage problems. In Studies in Applied Probability and Management Science (Arrow, , Karlin, , Scarf, , eds.) Stanford Univ. Press.Google Scholar
[2] Keilson, J. and Mermin, N. D. (1959) The second-order distribution of integrated shot noise. I.R.E. Trans. Inf. Th. 5, 75–77.Google Scholar
[3] Rice, S. O. (1954) Mathematical analysis of random noise. In Selected Papers on Noise and Stochastic Processes (Wax, N., ed.), Dover, New York.Google Scholar
[4] SahiN, I. (1971) Equilibrium behavior of a stochastic system with secondary input. J. Appl. Prob. 8, 252–260.Google Scholar
[5] Takács, L. (1963) The limiting distribution of the virtual waiting time and the queue size for a single server queue with recurrent input and general service times. Sankhya, A 25, 91–100.Google Scholar
[6] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes, Wiley, New York.Google Scholar
[7] Takács, L. (1955) On stochastic processes connected with certain physical recording apparatuses. Acta Math. Acad. Sci. Hung. 5, 363–380.Google Scholar
[8] Takács, L. (1954) On secondary processes generated by a Poisson process and their applications in physics. Acta Math. Acad. Sci. Hung. 5, 203–236.Google Scholar