Showing papers by "Antonio Di Crescenzo published in 2002"

Entropy-based measure of uncertainty in past lifetime distributions

Abstract: As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

On prices' evolutions based on geometric telegrapher's process

Abstract: The geometric telegrapher's process is proposed as a model to describe the dynamics of the price of risky assets. When the underlying random inter-times have Erlang distribution we express the probability law of such process in terms of a suitable two-index pseudo-Bessel function. Stochastic comparisons of two geometric telegrapher's processes based on the usual stochastic order (FSD comparison) and on the stop-loss order are also performed. Various examples of application of such comparisons are then provided. Copyright © 2002 John Wiley & Sons, Ltd.

Exact transient analysis of a planar random motion with three directions

Abstract: Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of direction perform an alternating renewal process. We obtain the probability law of the bidimensional stochastic process which describes location and direction of the motion. In the Markovian case when the random times between consecutive changes of direction are exponentially distributed, the transition densities of the motion are explicitly given. These are expressed in term of a suitable modified two-index Bessel function.

Input-output behaviour of a model neuron with alternating drift

Abstract: The input-output behaviour of the Wiener neuronal model subject to alternating input is studied under the assumption that the effect of such an input is to make the drift itself of an alternating type. Firing densities and related statistics are obtained via simulations of the sample-paths of the process in the following three cases: the drift changes occur during random periods characterised by (i) exponential distribution, (ii) Erlang distribution with a preassigned shape parameter, and (iii) deterministic distribution. The obtained results are compared with those holding for the Wiener neuronal model subject to sinusoidal input.

Some results on degradation processes with repairs and catastrophes

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