On the Ritt property and weak type maximal inequalities for convolution powers on L1 (Z)

Christophe Cuny (1, 2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 ERIM - Equipe de Recherche en Informatique et Mathématiques

In this paper we study the behaviour of convolution powers of probability measures µ on Z, such that (µ(n)) n∈N is completely monotone or such that ν is centered with a second moment. In particular we exhibit many new examples of probability measures on Z having the so called Ritt property and whose convolution powers satisfy weak type maximal inequalities in L1 (Z).

Domaines: Probabilités [math.PR]

Christophe Cuny. On the Ritt property and weak type maximal inequalities for convolution powers on L1 (Z). Studia Mathematica, 2016, 235 (1), pp.47-85. ⟨10.4064/sm8516-8-2016⟩. ⟨hal-01261292⟩