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For a binary stationary time series define $σ_{n}$ to be the number of consecutive ones up to the first zero encountered after time $n$ , and consider the problem of estimating the conditional distribution and conditional expectation of $σ_{n}$ after one has observed the first $n$ outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state...

Infinite queueing systems with tree structure

Lucie Fajfrová (2006)

Kybernetika

We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set $ℤ^{d}$ . We have chosen the tree structure with the dynamics that leads to one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number...

Infinite system of Brownian balls with interaction: the non-reversible case

Myriam Fradon, Sylvie Rœlly (2007)

ESAIM: Probability and Statistics

We consider an infinite system of hard balls in $^{d}$ undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.

Infinite trees and inverse gaussian random variables

Ole E. Barndorff-Nielsen, Tina Hviid Rydberg (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Infinite volume asymptotics of the ground state energy in a scaled poissonian potential

Franz Merkl, Mario V. Wüthrich (2002)

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

Information recovery from randomly mixed-up message text.

Lember, Jüri, Matzinger, Heinrich (2008)

Electronic Journal of Probability [electronic only]

Intégrabilité des temps de renouvellement des files d'attente et applications

François Charlot (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

Integrability of exit times and ballisticity for random walks in Dirichlet environment.

Tournier, Laurent (2009)

Electronic Journal of Probability [electronic only]

Interacting brownian particles and Gibbs fields on pathspaces

David Dereudre (2003)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Interacting Brownian particles and Gibbs fields on pathspaces

David Dereudre (2010)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Interlacement percolation on transient weighted graphs.

Teixeira, Augusto (2009)

Electronic Journal of Probability [electronic only]

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