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1 April 2008

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

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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
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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}.

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