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Author

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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors investigated large deviation problems for a random walk in continuous time with spatially inhomogeneous rates of alternating type and obtained an asymptotic lower bound for level crossing probabilities.
Abstract: We investigate some large deviation problems for a random walk in continuous time \(\{N(t);\,t\ge 0\}\) with spatially inhomogeneous rates of alternating type. We first deal with the large deviation principle for the convergence of \(N(t)/t\) to a suitable constant. Then, the case of moderate deviations is also discussed. Motivated by possible applications in chemical physics context, we finally obtain an asymptotic lower bound for level crossing probabilities both in the case of finite and infinite horizon.

14 citations

Journal ArticleDOI
TL;DR: In this article, a quantile-based probabilistic mean value theorem was proposed for nonnegative random variables with nonnegative residual-lifetime distributions. But the quantile function is not a generalization of the cumulative distribution function.
Abstract: For nonnegative random variables with finite means we introduce an analogous of theequilibrium residual-lifetime distribution based on the quantile function. This allows toconstruct new distributions with support (0,1), and to obtain a new quantile-based versionof the probabilistic generalization of Taylor’s theorem. Similarly, for pairs of stochasticallyordered random variables we come to a new quantile-based form of the probabilistic meanvalue theorem. The latter involves a distribution that generalizes the Lorenz curve. Weinvestigate the special case of proportional quantile functions and apply the given resultsto various models based on classes of distributions and measures of risk theory. Motivatedby some stochastic comparisons, we also introduce the ‘expected reversed proportionalshortfall order’, and a new characterization of random lifetimes involving the reversedhazard rate function.Short title: A quantile-based probabilistic mean value theorem. 1 Introduction The quantile function, being the inverse of the cumulative distribution function of a randomvariable, is often invoked in applied probability and statistics. In certain cases the approachbased on quantile functions is more fruitful than the use of cumulative distribution functions,since quantile functions are less influenced by extreme statistical observations. For instance,quantile functions can be properly employed to formulate properties of entropy function and

13 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the distribution of the location at time t of a particle moving U time units upwards, V time units downwards, and W time units of no movement (idle).
Abstract: In this paper we study the distribution of the location, at time t , of a particle moving U time units upwards, V time units downwards, and W time units of no movement (idle). These are repeated cyclically, according to independent alternating renewals. The distributions of U , V , and W are absolutely continuous. The velocities are v = +1 upwards, v = -1 downwards, and v = 0 during idle periods. Let Y + ( t ), Y − ( t ), and Y 0 ( t ) denote the total time in (0, t ) of movements upwards, downwards, and no movements, respectively. The exact distribution of Y + ( t ) is derived. We also obtain the probability law of X ( t ) = Y + ( t ) - Y − ( t ), which describes the particle's location at time t . Explicit formulae are derived for the cases of exponential distributions with equal rates, with different rates, and with linear rates (leading to damped processes).

13 citations

Journal ArticleDOI
TL;DR: In this paper, the conditional density and the mean of a new diffusion process Y(t) with the same state-space and the same infinitesimal variance, whose drift depends on the infiniteimal moments of X(t), and on the hazard rate function of Z.
Abstract: Let X(t) be a time-homogeneous diffusion process with state-space $$[0,+\infty )$$ , where 0 is a reflecting or entrance endpoint, and let Z denote a random variable that describes the process X(t) evaluated at an exponentially distributed random time. We propose a method to obtain closed-form expressions for the conditional density and the mean of a new diffusion process Y(t), with the same state-space and with the same infinitesimal variance, whose drift depends on the infinitesimal moments of X(t) and on the hazard rate function of Z. This method also allows us to obtain the Laplace transform of the first-passage-time density of Y(t) through a lower constant boundary. We then discuss the relation between Y(t) and the process X(t) subject to catastrophes, as well as the interpretation of Y(t) as a diffusion in a decreasing potential. We study in detail some special cases concerning diffusion processes obtained when X(t) is the Wiener, Ornstein–Uhlenbeck, Bessel and Rayleigh process.

13 citations

Journal ArticleDOI
TL;DR: In this article, the first-passage-time problem for a compound Poisson process characterized by independent, identically and exponentially distributed jumps, occurring according to the power-law process (PLP), is considered.
Abstract: We consider a first-passage-time problem for a compound Poisson process characterized by independent, identically and exponentially distributed jumps, occurring according to the power-law process (PLP). First of all, we refer to the conditional product moments of arrival times and to the interarrival times density of a power-law process. We then obtain the probability density of the crossing time through a linear boundary at the occurrence of the nth jump. In particular, we express the first-passage-time density in terms of a conditional expectation involving the arrival times.

12 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