Système de processus auto-stabilisants

Samuel Herrmann

  • 2003

Abstract

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Taking an odd increasing Lipschitz-continuous function with polynomial growth β, an odd Lipschitz-continuous and bounded function ϕ satisfying sgn(x)ϕ(x) ≥ 0 and a parameter a ∈ [1/2,1], we consider the (nonlinear) stochastic differential system ⎧ X t = X ₀ + B t + a ∫ 0 t ϕ * v s ( X s ) d s - ( 1 - a ) ∫ 0 t β * u s ( X s ) d s , (E)⎨ ⎩ Y t = Y ₀ + B ̃ t + ( 1 - a ) ∫ 0 t ϕ * u s ( Y s ) d s - a ∫ 0 t β * v s ( Y s ) d s , ℙ ( X t ∈ d x ) = u t ( d x ) and ℙ ( Y t ∈ d x ) = v t ( d x ) , where β * u t ( x ) = ∫ ℝ β ( x - y ) u t ( d y ) , ( B t ) t ≥ 0 and ( B ̃ t ) t ≥ 0 are independent Brownian motions. We show that (E) admits a stationary probability measure, and, under some additional conditions, that ( X t , Y t ) converges in distribution to this invariant measure. Moreover we investigate the link between (E) and the associated system of particles.

How to cite

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Samuel Herrmann. Système de processus auto-stabilisants. 2003. <http://eudml.org/doc/285971>.

@book{SamuelHerrmann2003,
author = {Samuel Herrmann},
language = {fre},
title = {Système de processus auto-stabilisants},
url = {http://eudml.org/doc/285971},
year = {2003},
}

TY - BOOK
AU - Samuel Herrmann
TI - Système de processus auto-stabilisants
PY - 2003
LA - fre
UR - http://eudml.org/doc/285971
ER -

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