Define the scaled empirical point process on an independent and identically distributed sequence {Yi : i ≤ n} as the random point measure with masses at a n Yi. For suitable an we obtain the weak limit of these point processes through a novel use of a dimension-free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several dire...

and Applied Analysis 3 where the first term refers to the probability mass concentrated in the origin, δ y denotes the Dirac delta function, and fYβ denotes the density of the absolutely continuous component. The function gYβ given in 1.5 satisfies the following fractional master equation, that is, ∂ ∂tβ gYβ ( y, t ) −λgYβ ( y, t ) λ ∫ ∞ −∞ gYβ ( y − x, t ) fX x dx, 1.6 where ∂/∂t is the Caputo...

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyz...

Several classes of nonparametric priors are employed to model the rate of occurrence of failures of the nonhomogeneous Poisson process used in software reliability or in repairable systems. The classes include the gamma process prior, the beta process prior, and the extended gamma process prior. We derive the posterior distribution for each process. Sampling based methods are developed for Baye...

Let Π and Γ be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Π and Γ such that Γ is a deterministic function of Π, and all points of Γ are points of Π. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exi...

Multivariate Poisson processes have many important applications in Insurance, Finance, and many other areas of Applied Probability. In this paper we study the backward simulation approach to modelling multivariate Poisson processes and analyze the connection to the extreme measures describing the joint distribution of the processes at the terminal simulation time.

This paper considers the problem of Bayesian inference in dynamical models with time-varying dimension. These models have been studied in the context of multiple target tracking problems and for estimating the number of components in mixture models. Traditional solutions for the single target tracking problem becomes infeasible when the number of targets grows. Furthermore, when the number of t...

The problem of parameter estimation and statistical inference when fitting an M/G/∞ queuing process to data is considered in the situation where the times of arrival and departure are unknown; instead recurrent events, which occur according to a mixed Poisson process, are observed between the times of arrival and departure.

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact same short term pattern every year, but lets its peak intensity vary over a longer period. This mode...

We present an algorithm which allows a fast numerical computation of Feldman-Cousins confidence intervals for Poisson processes, even when the number of background events is relatively large. This algorithm incorporates an appropriate treatment of the singularities that arise as a consequence of the discreteness of the variable.