Limit theorems for sequential expanding dynamical systems on [0,1]

Jean-Pierre Conze (1) , Albert Raugi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider the asymptotic behaviour of a sequence (theta(n)), theta(n) = tau(n) o tau(n - 1) . . . o tau(1), where (tau(n))(n >= 1) are non-singular transformations on a probability space. After briefly discussing some definitions and problems in this general framework, we consider the case of piecewise expanding transformations of the interval. Exactness and statistical properties (a central limit theorem for BV functions after a moving centering) can be shown for some families of such transformations. The method relies on an extension of the spectral theory of transfer operators to the case of a sequence of transfer operators.

Mots clés: sequential dynamical systems; expanding maps; transfer operator

Domaines: Probabilités [math.PR]

Jean-Pierre Conze, Albert Raugi. Limit theorems for sequential expanding dynamical systems on [0,1]. Contemporary mathematics, 2007, 430, pp.89-121. ⟨hal-00365220⟩