618 research outputs found
A Parrondo Paradox in Reliability Theory
Parrondo's paradox arises in sequences of games in which a winning
expectation may be obtained by playing the games in a random order, even though
each game in the sequence may be lost when played individually. We 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. If the first system is modified so that the distributions of its
new units are mixtures of the previous distributions with equal probabilities,
then under suitable conditions the new system is shown to be more reliable than
the second in the "usual stochastic order" sense.Comment: 6 page
On jump-diffusion processes with regime switching: martingale approach
We study jump-diffusion processes with parameters switching at random times.
Being motivated by possible applications, we characterise equivalent martingale
measures for these processes by means of the relative entropy. The minimal
entropy approach is also developed. It is shown that in contrast to the case of
L\'evy processes, for this model an Esscher transformation does not produce the
minimal relative entropy.Comment: 23 pages, 2 figure
A review on symmetry properties of birth-death processes
In this paper we review some results on time-homogeneous birth-death
processes. Specifically, for truncated birth-death processes with two absorbing
or two reflecting endpoints, we recall the necessary and sufficient conditions
on the transition rates such that the transition probabilities satisfy a
spatial symmetry relation. The latter leads to simple expressions for
first-passage-time densities and avoiding transition probabilities. This
approach is thus thoroughly extended to the case of bilateral birth-death
processes, even in the presence of catastrophes, and to the case of a
two-dimensional birth-death process with constant rates.Comment: 16 pages, 4 figure
On the Effect of Random Alternating Perturbations on Hazard Rates
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.Comment: 14 pages, 6 figure
Extension of the past lifetime and its connection to the cumulative entropy
Given two absolutely continuous nonnegative independent random variables, we
define the reversed relevation transform as dual to the relevation transform.
We first apply such transforms to the lifetimes of the components of parallel
and series systems under suitably proportionality assumptions on the hazards
rates. Furthermore, we prove that the (reversed) relevation transform is
commutative if and only if the proportional (reversed) hazard rate model holds.
By repeated application of the reversed relevation transform we construct a
decreasing sequence of random variables which leads to new weighted probability
densities. We obtain various relations involving ageing notions and stochastic
orders. We also exploit the connection of such a sequence to the cumulative
entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative
formulae for computing the mean and the cumulative entropy of the random
variables of the sequence are finally investigated
On a bilateral birth-death process with alternating rates
We consider a bilateral birth-death process characterized by a constant
transition rate from even states and a possibly different transition
rate from odd states. We determine the probability generating functions
of the even and odd states, the transition probabilities, mean and variance of
the process for arbitrary initial state. Some features of the birth-death
process confined to the non-negative integers by a reflecting boundary in the
zero-state are also analyzed. In particular, making use of a Laplace transform
approach we obtain a series form of the transition probability from state 1 to
the zero-state.Comment: 13 pages, 3 figure
Compound Poisson process with a Poisson subordinator
A compound Poisson process whose randomized time is an independent Poisson
process is called compound Poisson process with Poisson subordinator. We
provide its probability distribution, which is expressed in terms of the Bell
polynomials, and investigate in detail both the special cases in which the
compound Poisson process has exponential jumps and normal jumps. Then for the
iterated Poisson process we discuss some properties and provide convergence
results to a Poisson process. The first-crossing-time problem for the iterated
Poisson process is finally tackled in the cases of (i) a decreasing and
constant boundary, where we provide some closed-form results, and (ii) a
linearly increasing boundary, where we propose an iterative procedure to
compute the first-crossing-time density and survival functions.Comment: 16 pages, 7 figure
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