Antonio Di Crescenzo

Bio: Antonio Di Crescenzo is an academic researcher from University of Salerno. The author has contributed to research in topics: Stochastic process & Telegraph process. The author has an hindex of 22, co-authored 139 publications receiving 1944 citations. Previous affiliations of Antonio Di Crescenzo include University of Basilicata.

A Continuous-Time Ehrenfest Model with Catastrophes and Its Jump-Diffusion Approximation

Abstract: We consider a continuous-time Ehrenfest model defined over the integers from $$-N$$ to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe istantaneously resets the process to state 0. We investigate both the transient and steady-state probabilities of the above model. Further, the first passage time through state 0 is discussed. We perform a jump-diffusion approximation of the above model, which leads to the Ornstein-Uhlenbeck process with catastrophes. The underlying jump-diffusion process is finally studied, with special attention to the symmetric case arising when the Ehrenfest model has equal upward and downward transition rates.

Diffusion approximation to a queueing system with time-dependent arrival and service rates

Abstract: A time nonhomogeneous diffusion approximation to a single server-single queue service system is obtained. Under various assumptions on the time-dependent functions appearing in the infinitesimal moments, transient and steady-state behaviour are analyzed. In particular, a diffusion approximation characterized by space-linear and time-varying moments is studied. The density of the busy period and the probability for the busy period to terminate are obtained. Finally, estimates of the goodness of the diffusion approximation are given.

A probabilistic analogue of the mean value theorem and its applications to reliability theory

Abstract: In a similar spirit to the probabilistic generalization of Taylor's theorem by Massey and Whitt [13], we give a probabilistic analogue of the mean value theorem. The latter is shown to be useful in various contexts of reliability theory. In particular, we provide various applications to the evaluation of the mean total profits of devices having random lifetimes, to the mean total-time-on-test at an arbitrary order statistic of a random sample of lifetimes, and to the mean maintenance cost for the second room of queueing systems in steady state characterized by two serial waiting rooms.

A parrondo paradox in reliability theory

Abstract: Dipartimento di Matematica e InformaticaUniversit`a di Salerno84084 Fisciano (SA), ItalyE-mail: adicrescenzo@unisaitAbstractParrondo’s paradox arises in sequences of games in which a winning expectation may beobtained by playing the games in a random order, even though each game in the sequencemay be lost when played individually We present a suitable version of Parrondo’s paradoxin reliability theory involving two systems in series, the units of the first system being lessreliable than those of the second If the first system is modified so that the distributions ofits new units are mixtures of the previous distributions with equal probabilities, then undersuitable conditions the new system is shown to be more reliable than the second in the “usualstochastic order” sense

Exact transient analysis of a planar random motion with three directions

Abstract: Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of direction perform an alternating renewal process. We obtain the probability law of the bidimensional stochastic process which describes location and direction of the motion. In the Markovian case when the random times between consecutive changes of direction are exponentially distributed, the transition densities of the motion are explicitly given. These are expressed in term of a suitable modified two-index Bessel function.

Table Of Integrals Series And Products

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Applied Probability and Queues

Abstract: (1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.