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Showing papers by "Antonio Di Crescenzo published in 2007"


Posted Content
TL;DR: In this paper, the authors present a suitable version of Parrondo's paradox in reliability theory involving two systems in series, the units of the first system being less reliable than those of the second.
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

35 citations


Journal ArticleDOI
TL;DR: A stochastic model for the firing activity of a neuronal unit that includes the decay effect of the membrane potential in absence of stimuli, and the occurrence of time-varying excitatory inputs governed by a Poisson process is proposed.
Abstract: We propose a stochastic model for the firing activity of a neuronal unit. It includes the decay effect of the membrane potential in absence of stimuli, and the occurrence of time-varying excitatory inputs governed by a Poisson process. The sample-paths of the membrane potential are piecewise exponentially decaying curves with jumps of random amplitudes occurring at the input times. An analysis of the probability distributions of the membrane potential and of the firing time is performed. In the special case of time-homogeneous stimuli the firing density is obtained in closed form, together with its mean and variance.

12 citations


Book ChapterDOI
12 Feb 2007
TL;DR: A generalized integrated telegraph process is analyzed, where the random times between consecutive velocity reversals are gamma-distributed, and the probability law and the mean are obtained.
Abstract: Motivated by applications in mathematical biology concerning randomly alternatingmotion ofmicro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are gamma-distributed, and perform an alternating renewal process. We obtain the probability law and the mean of the process.

9 citations


Posted Content
TL;DR: In this paper, a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables is introduced.
Abstract: We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables This allows us to introduce the notions of "weighted residual entropy" and "weighted past entropy", that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively The obtained results include their behaviors under monotonic transformations

9 citations


Posted Content
TL;DR: In this paper, a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process, is considered.
Abstract: We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided.

3 citations


Posted Content
TL;DR: In this article, the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process is considered, and lower bounds for the first cross-time density and distribution function are obtained.
Abstract: We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit lower bounds for the first-crossing-time density and for the first-crossing-time distribution function. In the case of the distribution function, the bound is improved by use of processes comparison based on the usual stochastic order. The special case of constant jumps driven by a Poisson process is thoroughly discussed.