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In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X (t), t ≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration(More)
We consider some fractional extensions of the recursive differential equation governing the Pois-son process, i.e. d d t p k (t) = −λ(p k (t) − p k−1 (t)), k ≥ 0, t > 0 by introducing fractional time-derivatives of order ν, 2ν, ..., nν. We show that the so-called " Generalized Mittag-Leffler functions " E k α,β (x), x ∈ (introduced by Prabhakar [24]) arise(More)
We consider a fractional version of the classical non-linear birth process of which the Yule-Furry model is a particular case. Fractionality is obtained by replacing the first-order time derivative in the difference-differential equations which govern the probability law of the process, with the Dzherbashyan-Caputo fractional derivative. We derive the(More)
Statistics and Probability Letters xx (xxxx) xxx–xxx Available online xxxx MSC: 60G18 60J80 a b s t r a c t The descending motion of particles in a Sierpinski gasket subject to a branching process is examined. The splitting on escape nodes of falling particles makes the event of reaching the base of the gasket possible with positive probability. The r.v.'s(More)
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