Itérations des Fonctions aléatoires et application à la simulation

Bessad, B.; Ladjimi, F.; Boudiba, Mohamed Arezki

Séminaire Mathématique de Béjaia
Volume 12, Numéro 1, Pages 115-120
2013-12-31

Itérations Des Fonctions Aléatoires Et Application à La Simulation

Authors : Bessad B. . Ladjimi F. . Boudiba Mohamed Arezki .

Abstract

The purpose is some observations on the Markov Chains (Xxn)n, on the model Xxn = Fn◦Fn−1 • • •◦F1(x), where (Fn)n is a sequence of i.i.d. random functions. We discribe a motivating example related to the growth of a population. We state a result on the limits of (Xxn)n in the particular case where the Fn are generated by the functions fY,(x) = k(Yn) + g(x) with (Yn)n a sequence of i.i.d. random variables and where k and g are some suitable functions. We end our exposition by a survey of general theory and an application of such models to exact simulation algorithm of Propp-Wilson. We notice in the conclusion the relationsheep with the recurrency class of the backward chain functions, for the “coalescence” time to be finite.