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 published on a yearly basis
Papers
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01 Jan 1991
1 citations
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14 Feb 2019
TL;DR: In this article, the authors discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy, and prove a central limit theorem for the empirical cumulative measure under exponentially distributed populations.
Abstract: In this paper, we discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy. We also present some properties of the proposed measures, and the empirical cumulative measure of inaccuracy in k-lower record values. We prove a central limit theorem for the empirical cumulative measure of inaccuracy under exponentially distributed populations. Finally, we analyze the mutual information for measuring the degree of dependency between lower record values, and we show that it is distribution-free.
1 citations
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TL;DR: In this paper, a fractional jump process with jumps of size 1 and 2 was considered, whose probabilities satisfy the fractional extension of the difference-differential equations, and the probability law of the resulting process was obtained in terms of generalized Mittag-Leffler functions.
Abstract: We consider a fractional jump process with jumps of size 1 and 2, whose probabilities satisfy a fractional extension of the difference-differential equations $$ \dfrac{\mathrm{d}p_{k}(t) }{\mathrm{d}t } =\lambda_{2}p_{k-2}(t)+\lambda_{1}p_{k-1}(t)-(\lambda_{1}+\lambda_{2})p_{k}(t), \quad k\geq 0, \;\; t>0. $$ We obtain the probability law of the resulting process in terms of generalized Mittag-Leffler functions. We also discuss two equivalent representations both in terms of a subordinator governed by a suitable fractional Cauchy problem, and of a compound fractional Poisson process. 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 result for the Poisson process. We also express the distribution of the first passage time of the fractional jump process in an integral form that involves the joint distribution of the classical fractional Poisson process. Finally, we show that the ratios given by the powers of the jump process over their means converge in probability to 1.
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TL;DR: In this paper, the jump telegraph process was considered and the incomplete financial market model based on this process was studied, which can price switching risks as well as jump risks of the model.
Abstract: We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model.
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28,685 citations
01 Jan 2016
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4,085 citations
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1,188 citations
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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