A moment approach for the almost sure central limit theorem for martingales

Bernard Bercu (1, 2) , Jean-Claude Fort (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 LSP - Laboratoire de Statistique et Probabilités

We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments for powers of martingales. Several statistical applications on autoregressive and branching processes are also provided.

Mots clés: Martingale transforms; Moments

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Bernard Bercu, Jean-Claude Fort. A moment approach for the almost sure central limit theorem for martingales. Studia Scientiarum Mathematicarum Hungarica, 2008, 45, pp.139-159. ⟨hal-00012679⟩