Products of Beta matrices and sticky flows

Yves Le Jan (1) , Sophie Lemaire (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

A discrete model of Brownian sticky flows on the unit circle is described: it is constructed with products of Beta matrices on the discrete torus.Sticky flows are defined by their "moments'' which are consistent systems of transition kernels on the unit circle. Similarly, the moments ofthe discrete model form a consistent system of transition matrices on the discrete torus. A convergence of Beta matrices to sticky kernels is shown at the levelof the moments.

Mots clés: Markov chains with continuous parameter; Polya urns; stochastic flow of kernels; Feller semigroups; convergence of resolvents

Domaines: Probabilités [math.PR]

Yves Le Jan, Sophie Lemaire. Products of Beta matrices and sticky flows. 2003. ⟨hal-00000491v1⟩