Showing papers by "Barbara Martinucci published in 2013"
TL;DR: In this paper, the authors considered a semi-Markovian generalization of the integrated telegraph process subject to jumps and obtained the formal expressions of the forward and backward transition densities of the motion.
Abstract: We consider a semi-Markovian generalization of the integrated telegraph process subject to jumps. It describes a motion on the real line characterized by two alternating velocities with opposite directions, where a jump along the alternating direction occurs at each velocity reversal. We obtain the formal expressions of the forward and backward transition densities of the motion. We express them as series in the case of Erlang-distributed random times separating consecutive jumps. Furthermore, a closed form of the transition density is given for exponentially distributed times, with constant jumps and random initial velocity. In this case we also provide mean and variance of the process, and study the limiting behaviour of the probability law, which leads to a mixture of three Gaussian densities.
29 citations
TL;DR: In this article, the authors considered a generalized telegraph process which follows an alternating renewal process and is subject to random jumps, and developed the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times.
Abstract: We consider a generalized telegraph process which follows an alternating renewal process and is subject to random jumps. More specifically, consider a particle at the origin of the real line at time t=0. Then it goes along two alternating velocities with opposite directions, and performs a random jump toward the alternating direction at each velocity reversal. We develop the distribution of the location of the particle at an arbitrary fixed time t, and study this distribution under the assumption of exponentially distributed alternating random times. The cases of jumps having exponential distributions with constant rates and with linearly increasing rates are treated in detail.
27 citations
TL;DR: In this paper, the authors considered a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions, and investigated the probability law of the process and the mean of the velocity of the moving particle.
Abstract: We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Polya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of Polya trials and intertimes having first Gamma and then exponential distributions with constant rates.
18 citations
TL;DR: An extension of the spike train stochastic model based on the conditional intensity, in which the recovery function includes an interaction between several excitatory neural units is investigated, to obtain the general form of the interspike distribution and of the probability of consecutive spikes from the same unit.
Abstract: We investigate an extension of the spike train stochastic model based on the conditional
intensity, in which the recovery function includes an interaction between several excitatory
neural units. Such function is proposed as depending both on the time elapsed since the
last spike and on the last spiking unit. Our approach, being somewhat related to the
competing risks model, allows to obtain the general form of the interspike distribution and
of the probability of consecutive spikes from the same unit. Various results are finally presented
in the two cases when the free firing rate function (i) is constant, and (ii) has a sinusoidal form.
1 citations
TL;DR: In this paper, the authors considered a bilateral birth-death process characterized by a constant transition rate from even states and a possibly different transition rate in odd states. And they derived the probability generating functions of the even and odd states, the transition probabilities, mean and variance of the process for arbitrary initial state.
Abstract: We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ 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.
IAC1
TL;DR: The model of random evolution on the real line consisting in a Brownian motion perturbed by alternating jumps is considered, and the probability density is given and a connection is pinpointed with the limit density of a telegraph process subject to alternating jumps.
Abstract: We consider the model of random evolution on the real line consisting in a Brownian motion perturbed by alternating jumps. We give the probability density of the process and pinpoint a connection with the limit density of a telegraph process subject to alternating jumps. We study the first-crossing-time probability in two special cases, in the presence of a constant upper boundary.