Related papers: Correlated fractional counting processes on a fini…

There is a well established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times,…

An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…

A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…

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…

In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…

In this paper, we define a fractional negative binomial process (FNBP) by replacing the Poisson process by a fractional Poisson process (FPP) in the gamma subordinated form of the negative binomial process. First, it is shown that the…

We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…

In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance \int_0^{s\wedge t} u^a [(t-u)^b+(s-u)^b]du, parameters a>-1, -1<b\leq 1, |b|\leq 1+a, corresponds to fractional Brownian…

In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to…

Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to infinity. The limit distribution is non-standard and differs…

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.

We study the connection between PDEs and L\'{e}vy processes running with clocks given by time-changed Poisson processes with stochastic drifts. The random times we deal with are therefore given by time-changed Poissonian jumps related to…

We study quantitative recurrence to rare events in Countable Markov Shifts with recurrent potentials, focusing on return-time statistics to natural target sets for every point. In the positive recurrent case, return-time processes…

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…

We study the distribution of normalized spacings between the fractional parts of an^2, n=1,2,.... We conjecture that if a is "badly approximable" by rationals, then the sequence of fractional parts has Poisson spacings, and give a number of…

The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\nu_k}(t)$, $t\ge 0$, are governed by time-fractional equations of order $0<\nu_k\leq 1$ depending on the number $k$ of events…

A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…

We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172--182] for sums of uniformly null…

We study a compound Poisson random field on plane and examine its various fractional variants. We derive the distributions of these random fields and in some particular cases, obtain their associated system of governing differential…

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…