Limit law for some modified ergodic sums

Jean-Pierre Conze (1) , Stéphane Le Borgne (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

An example due to Erdos and Fortet shows that, for a lacunary sequence of integers (q_n) and a trigonometric polynomial f, the asymptotic distribution of normalized sums of f(q_k x) can be a mixture of gaussian laws. Here we give a generalization of their example interpreted as the limiting behavior of some modified ergodic sums in the framework of dynamical systems.

Mots clés: Modified ergodic sums; asymptotic distribution; group action; multiple decorrelation

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Jean-Pierre Conze, Stéphane Le Borgne. Limit law for some modified ergodic sums. Stochastics and Dynamics, 2011, 11 (1), pp.107-133. ⟨10.1142/S021949371100319X⟩. ⟨hal-00450631v2⟩