Numérotation Des Records D'un Processus de Poisson Ponctuel (French) [The Numbering of Records of a Poisson Point Process]

The Favorite Point of a Poisson Process

In this paper we consider the most visited site, Xt, of a Poisson process up to time t. Our point of departure from the literature on maximal spacings is our asymptotic analysis of where the maximal spacing occurs (i.e., the size of Xt) and not the size of the spacings.

On the modelling of wireless communication networks using non-poisson point processes. (Sur la modélisation des réseaux de communication sans fil en utilisant les processus ponctuels non-poisson)

Corners and Records of the Poisson Pro- Cess in Quadrant

The scale-invariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant.

Fractional Poisson Process

For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these p...

Navigation on a Poisson Point Process

On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on R. We examine the local weak convergence of the navigation tree, the asymptotic average of a func...