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Article

On the Distributions of a Renewal Reward Process and It’s Additive Functional

by
Tahir Khaniyev
1,3,*,
Rovshan Aliyev
1,3,
Zafer Küçük
1 and
Nurgul Okur Bekar
2
1
Karadeniz Technical University, Faculty of Arts and Sciences, Department of Statistics and Computer Sciences, 61080, Trabzon, Turkey
2
Karadeniz Technical University, Faculty of Arts and Sciences, Department of Mathematics, 61080, Trabzon, Turkey
3
Institute of Cybernetics of Azerbaijan National Academy of Sciences, F. Agayev str.9, Az 1141, Baku, Azerbaijan
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2008, 13(1), 41-50; https://doi.org/10.3390/mca13010041
Published: 1 April 2008
Versions Notes

Abstract

In this study, a renewal reward process with a discrete interference of chance (X(t)) is constructed and distribution of the process X(t) is investigated. One dimensional distribution of the process X(t) is given by means of the probability characteristics of the renewal processes {Tn } and {Sn }. Moreover, one dimensional distribution function of the additive functional Jf(t) of the process X(t) is expressed by the probability characteristics of the initial sequences of the random variables {ξn} and {ηn}.
Keywords: Renewal Reward Process; Additive Functional; Finite DimensionalDistribution; Discrete Interference of Chance Renewal Reward Process; Additive Functional; Finite DimensionalDistribution; Discrete Interference of Chance

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MDPI and ACS Style

Khaniyev, T.; Aliyev, R.; Küçük, Z.; Bekar, N.O. On the Distributions of a Renewal Reward Process and It’s Additive Functional. Math. Comput. Appl. 2008, 13, 41-50. https://doi.org/10.3390/mca13010041

AMA Style

Khaniyev T, Aliyev R, Küçük Z, Bekar NO. On the Distributions of a Renewal Reward Process and It’s Additive Functional. Mathematical and Computational Applications. 2008; 13(1):41-50. https://doi.org/10.3390/mca13010041

Chicago/Turabian Style

Khaniyev, Tahir, Rovshan Aliyev, Zafer Küçük, and Nurgul Okur Bekar. 2008. "On the Distributions of a Renewal Reward Process and It’s Additive Functional" Mathematical and Computational Applications 13, no. 1: 41-50. https://doi.org/10.3390/mca13010041

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