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.

Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.

Abstract: We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a linear time-inhomogeneous birth-death process whose mean behaves as the deterministic one. We obtain the transition probabilities, the moments and the population ultimate extinction probability for this process. We finally treat the special case of a simple birth process, which better mimics the proposed growth model.

Generalized telegraph process with random jumps

Abstract: We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.

A fractional counting process and its connection with the Poisson process

Abstract: We consider a fractional counting process with jumps of amplitude 1,2,...,k, withk∈N, whoseprobabilitiessatisfy a suitablesystemoffractionaldifference-differential equations. We obtain the moment generating function and the probability law of the result- ing process in terms of generalized Mittag-Leffler functions. We also discuss two equiv- alent representations both in terms of a compound fractional Poisson process and of a subordinator governed by a suitable fractional Cauchy problem. The first occurrence time of a jump of fixed amplitude is proved to have the same distribution as the waiting time of the first event of a classical fractional Poisson process, this extending a well-known property of the Poisson process. When k = 2 we also express the distribution of the first passage time of the fractional counting process in an integral form. Finally, we show that the ratios given by the powers of the fractional Poisson process and of the countingprocess over their means tend to 1 in probability.

Compound Poisson process with a Poisson subordinator

Abstract: A compound Poisson process whose randomized time is an independent Poisson process is called a compound Poisson process with Poisson subordinator We provide its probability distribution, which is expressed in terms of the Bell polynomials, and investigate in detail both the special cases in which the compound Poisson process has exponential jumps and normal jumps Then for the iterated Poisson process we discuss some properties and provide convergence results to a Poisson process The first-crossing time problem for the iterated Poisson process is finally tackled in the cases of (i) a decreasing and constant boundary, where we provide some closed-form results, and (ii) a linearly increasing boundary, where we propose an iterative procedure to compute the first-crossing time density and survival functions

Further results on the generalized cumulative entropy

Abstract: Recently, a new concept of entropy called generalized cumulative entropy of order $n$ was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.

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.