1,721,015 research outputs found
On a finite-velocity random motion governed by a modified Euler-Poisson-Darboux equation
No full textTransient analysis of a birth-death process with alternating rates.
No full textA birth-death process on Z was proposed in [Conolly et al., 1997] to describe chain molecular diffusion. In that paper, the molecule
is modeled as an infinitely long chain of atoms joined by links subjected to random shocks which cause the atoms to move and
the molecule to diffuse. The shock mechanism is different according to whether the atom occupies an odd or an even position in the chain. Following the line of that model, we consider
a birth-death process on the whole set of integers, characterized by a constant transition rate from even states and a possibly
different rate from odd states. We determine the probability generating functions of even and odd states and then the transition probabilities of the process. Some features of the birth-death process confined to the nonnegative integers by the reflecting zero-state are also analyzed. In particular, making use
of a Laplace transform approach, we obtain the expression of the zero-state probability
Analysis of a stochastic neuronal model with excitatory inputs and state-dependent effects.
No full textWe 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
A damped telegraph random process with logistic stationary distribution
No full textWe introduce a stochastic process that describes a finite-velocity damped motion on the real line. Differently from the telegraph process, the random times between consecutive velocity changes have exponential distribution with linearly increasing parameters. We obtain the probability law of the motion, which admits a logistic stationary limit in a special case. Various results on the distributions of the maximum of the process and of the first passage time through a constant boundary are also given
On a first-passage-time problem for the compound power-law process
No full textWe consider a first-passage-time problem for a compound Poisson process characterized by
independent, identically and exponentially distributed jumps, occurring according to the
power-law process. First of all, we refer to the conditional product moments of arrival times
and to the interarrival times density of a power-law process. We then obtain the probability
density of the crossing time through a linear boundary at the occurrence of the n-th jump.
In particular, we express the first-passage-time density in terms of a conditional expectation
involving the arrival times
On the Generalized Telegraph Process with Deterministic Jumps
No full textWe 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
A review on symmetry properties of birth-death processes
No full textIn 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
A state-dependent stochastic neuronal model with periodic inputs
No full textA stochastic model for the firing activity of a neuronal unit has been recently proposed in
Di Crescenzo and Martinucci (2007). It includes the decay effect of the membrane potential
in the absence of stimuli, and the occurrence of time-varying excitatory inputs governed by
a Poisson process. We perform an analysis of this model in the case of time-non-homogeneous
excitatory stimuli arriving according to a periodic rate. The probability distribution of the
membrane potential is given in a closed form. We also develop a simulation-based
approach to study the firing density, together with the mean and the coefficient of
variation of the firing times
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