Related papers: A fractional counting process and its connection w…
We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and…
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
In this work we introduce correlated random walks on $\Z$. When picking suitably at random the coefficient of correlation, and taking the average over a large number of walks, we obtain a discrete Gaussian process, whose scaling limit is…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
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…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
In this paper, we define a compound generalized fractional counting process (CGFCP) which is a generalization of the compound versions of several well-known fractional counting processes. We obtain its mean, variance, and the fractional…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set $A \subset \mathbb{R}^d.$ This Poisson process of cylinders is…
Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some $k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$ generates a…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
This paper introduces the Non-homogeneous Generalized Skellam process (NGSP) and its fractional version NGFSP by time changing it with an independent inverse stable subordinator. We study distributional properties for NGSP and NGFSP…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
The explicit dynamics of the moments for the GKSL equation is obtained. In our case the GKSL equation corresponds to Poisson stochastic processes which lead to unitary jumps. We consider squeeze operators as the unitary jumps.