1,209 research outputs found
Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process
No full textA generalization of the classical Ornstein Uhlenbeck diffusion process including some deterministic time dependent functions in the infinitesimal moments is considered. The inference based on discrete sampling in time is provided by means of an iterative procedure that, in each step, combines the classical maximum likelihood estimation and a generalized method of moments. The validity of the suggested procedure is evaluated via a simulation study by considering several infinitesimal moments for the Ornstein Uhlenbeck type process and taking different sample size. Finally, an application to PM10 daily concentration in Turin metropolitan area in Italy is discussed
A state-dependent queueing system with asymptotic logarithmic distribution
No full textA Markovian single-server queueing model with Poisson arrivals and state- dependent service rates, characterized by a logarithmic steady-state distribution, is considered. The Laplace transforms of the transition probabilities and of the densities of the first-passage time to zero are explicitly evaluated. The performance measures are compared with those ones of the well-known M/M/1 queueing system. Finally, the effect of catastrophes is introduced in the model and the steady-state distribution, the asymptotic moments and the first-visit time density to zero state are determined
Inference of a Susceptible–Infectious stochastic model
No full textWe considered a time-inhomogeneous di usion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic
everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a non-homogeneous Wiener process so the probability distribution could be obtained.
Here we focused on the inference for such a process, by providing an estimation procedure for the involved parameters. We pointed out that the time dependence in the infinitesimal moments of the diffusion process made classical inference methods inapplicable. The proposed procedure were based
on the generalized method of moments in order to find a suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the maximum likelihood estimation was made, and cases in which the intensity function were time dependent with particular attention to periodic cases. Finally, we applied the estimation procedure to a
real dataset
Single neuron's activity: on certain problems of modeling and interpretation
No full textWith reference to the Ornstein-Uhlenbeck model for single neuron's activity, computational results and theoretical arguments are provided to discuss the goodness and the appropriateness of analytical approximations to first-passage-time densities and its moments. A gamma approximation is initially discussed, use of which is successively made to construct a probability density of a new form that appears to be particularly suitable to approximate the as yet unknown firing probability density function
Towards Dead Time Inclusion in Neuronal Modeling
No full textA mathematical description of the refractoriness period
in neuronal diffusion modeling is given and its moments
are explicitly obtained in a form that is suitable for quantitative
evaluations. Then, for the Wiener, Ornstein-Uhlenbeck and
Feller neuronal models, an analysis of the features exhibited by the mean and variance of
the first passage time and of refractoriness period is performed
On some diffusion approximations to queueing systems
No full textFor a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the system. Our approximating diffusion process includes the Wiener and the Ornstein-Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed for
On Neuronal Firing Modeling via Specially Confined Diffusion Processes
No full textFirst passage time problems for diffusion processes have been extensively investigated to' model neuronal firing activity or extinction times in population dynamics (see, for instance, [IO)). In this paper we study the asymptotic behavior of first passage times densities for a class of specially confined temporally homogeneous diffusion processes in the presence of an entrance or a reflecting boundary. The emphasis is on problems of a rather mathematical nature, concerning the behavior of the first passage time density and of its moments when the neuronal firing threshold is in the neighborhood of the reflecting boundary, and when it moves indefinitely away from it. Our asymptotic results are obtained without need to determine beforehand the transition probability density in the presence of entrance or reflecting boundariesj they depend, instead, only on drift, infinitesimal variance, threshold and on the entrance or the reflecting boundary of the processo Some evaluations of moments of first passage time, in particular, mean and variance, are performed by solving numerically, or analytically whenever possible, Siegert's recursion equations [12], and by comparing the results with those obtained through our approximate formulas. In the case where the transition probability density is known, the goodness of the obtained approximations can be verified. Such results appear to be useful for neuronal modeling in the presence of reversal potential especially to pinpoint the role of the involved parameters in various models, some of which are the object of a somewhat detailed analysis
A symmetry–based constructive approach to probability densities for one dimensional diffusion processes
No full textSpecial symmetry conditions on the transition p.d.f. of one dimensional
time-homogeneous diffusion processes with natural boundaries are investigated
and exploited to derive closed-form results concerning the transition p.d.f.'s
in the presence of absorbing and reflecting boundaries and the
first-passage-time
p.d.f. through time-dependent boundaries
On some time non homogeneous diffusion approximations to queueing systems
No full textTime-non-homogeneous diffusion approximations to single server-single queue-FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion spproximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the pdf of the busy period is seen to be unaffected by the presence of such periodicity
On the asymptotic behaviour of first–passage–time densities for one–dimensional diffusion processes and varying boundaries
No full textThe asymptotic behaviour of the first passage time (FPT) p.d.f.'s through certain time-varying boundaries, including periodic boundaries, is determined for a class of
one-dimensional diffusion processes with steady--state density. Sufficient conditions are given for the cases both of single and of pairs of asymptotically
constant and asymptotically periodic boundaries, under which the FPT densities asymptotically exhibit an
exponential behaviour. Explicit expressions are then worked out for the processes
that can be obtained from the Ornstein-Uhlenbeck process by spatial transformations.
Some new asymptotic results for the FPT density of the Wiener process are finally
proved together with a few miscellaneous results
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