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Article

Some Results on a Stochastic Process with a Discrete Chance Interference

Karadeniz Technical University, faculty of Arts and Sciences, Department of Mathematics, 61080, Trabzon, Turkey
Math. Comput. Appl. 1999, 4(2), 145-152; https://doi.org/10.3390/mca4020145
Published: 1 August 1999

Abstract

In this study, some problems connected with stochastic process with a discrete chance interference X(t) are investigated. In particular, one-dimensional distribution functions of the process are obtained and under some weak assumptions, the ergodic theorem for this process is given. As a result, the explicit form of ergodic distribution function is derived. Moreover, the double transform of distribution function of additive functional of the process X(t) is derived. Furthermore, asymptotic behaviour of the additive functional is investigated as t. Based on these results characteristic function of ergodic distribution of the process X(t) is obtained by using a joint distribution of random variables N and SN. In addition, the first and second moments of ergodic distribution of X(t) are expressed in terms of the moments of random variable N.

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MDPI and ACS Style

Khaniev, T.A. Some Results on a Stochastic Process with a Discrete Chance Interference. Math. Comput. Appl. 1999, 4, 145-152. https://doi.org/10.3390/mca4020145

AMA Style

Khaniev TA. Some Results on a Stochastic Process with a Discrete Chance Interference. Mathematical and Computational Applications. 1999; 4(2):145-152. https://doi.org/10.3390/mca4020145

Chicago/Turabian Style

Khaniev, T. A. 1999. "Some Results on a Stochastic Process with a Discrete Chance Interference" Mathematical and Computational Applications 4, no. 2: 145-152. https://doi.org/10.3390/mca4020145

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