Related papers: Some Compound Fractional Poisson Processes

We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…

We construct a compound Poisson process conditioned on its random summation that represents the sizes of the connected components in the sparse Erd\H{o}s-R\'enyi random graph $G(n,c/n)$. This new representation depicts a connection between…

In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines,…

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…

This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time…

We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…

We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…

In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear…

In this paper we study finite velocity planar random motions with an infinite number of possible directions, where the number of changes of direction is randomized by means of an inhomogeneous fractional Poisson distribution. We first…

We show that a Gibbs characterization of normalized generalized Gamma processes, recently obtained in Lijoi, Pr\"unster and Walker (2007), can alternatively be derived by exploiting a characterization of exponentially tilted Poisson-Kingman…

Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…

We study coarsening phenomena in three different simple exclusion processes with quenched disordered jump rates. In the case of the totally asymmetric process, an earlier phenomenological description is improved, yielding for the time…

We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for thelaws of random functionals of L\'evy processes or solutions of…

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL L\'evy processes and in particular establish a stochastic…

We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…

In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the…

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to L{\'e}vy processes in the Skorokhod space…

We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…