Displaying similar documents to “An algebraic approach to Pólya processes”

Strong law of large numbers for fragmentation processes

S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than for 1≥>0.

Branching Processes with Immigration and Integer-valued Time Series

Dion, J., Gauthier, G., Latour, A. (1995)

Serdica Mathematical Journal

Similarity:

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes...

A Ciesielski–Taylor type identity for positive self-similar Markov processes

A. E. Kyprianou, P. Patie (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

The aim of this note is to give a straightforward proof of a general version of the Ciesielski–Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski–Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly, a new transformation which maps a subset of the family of Laplace exponents of spectrally negative Lévy processes into itself. Secondly, some classical...

Limits of determinantal processes near a tacnode

Alexei Borodin, Maurice Duits (2011)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE...