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Antonio Di Crescenzo

Other affiliations: University of Basilicata
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.


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TL;DR: In this paper, the authors analyzed the one-dimensional telegraph random process confined by two boundaries, 0 and $H>0, and provided various results on the expected values of the renewal cycles and of the absorption time.
Abstract: We analyze the one-dimensional telegraph random process confined by two boundaries, 0 and $H>0$. The process experiences hard reflection at the boundaries (with random switching to full absorption). Namely, when the process hits the origin (the threshold $H$) it is either absorbed, with probability $\alpha$, or reflected upwards (downwards), with probability $1-\alpha$, for $0<\alpha<1$. We provide various results on the expected values of the renewal cycles and of the absorption time. The adopted approach is based on the analysis of the first-crossing times of a suitable compound Poisson process through linear boundaries. Our analysis includes also some comparisons between suitable stopping times of the considered telegraph process and of the corresponding diffusion process obtained under the classical Kac's scaling conditions.

1 citations

01 Jan 2002
TL;DR: In this article, the authors proposed a non-negative diffusion model for degradation, where the quality of a device is described by a nonnegative diffusion process starting at X(0) = x0 > 0, and the level X(t) = 0 stands for zero quality.
Abstract: A classical assumption in the theory of degradation models is that the quality of a device is described by a non-negative diffusion process {X(t), t ≥ 0} starting at X(0) = x0 > 0. Assuming that large values of X(t) correspond to a better quality, the level X(t) = 0 stands for zero quality, i.e. for the lack of functionality of the device. Consequently, the first-passage time T of {X(t)} through state zero gives the failure time of the device. We shall denote its probability density function (p.d.f.) by

1 citations

Journal ArticleDOI
TL;DR: For nonnegative random variables with finite means, this article introduced an analogous of the equilibrium residual-lifetime distribution based on the quantile function, which allows to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem.
Abstract: For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the `expected reversed proportional shortfall order', and a new characterization of random lifetimes involving the reversed hazard rate function.

1 citations


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01 Jan 2016
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

Book ChapterDOI
01 Jan 1998

1,532 citations

Journal ArticleDOI
TL;DR: In this paper, applied probability and queuing in the field of applied probabilistic analysis is discussed. But the authors focus on the application of queueing in the context of road traffic.
Abstract: (1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

1,121 citations