Burkholder's submartingales from a stochastic calculus perspective

Giovanni Peccati (1) , Marc Yor (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in terms of a squared Brownian motion and of some appropriate powers of its maximum. Our techniques involve elementary stochastic calculus, as well as the Doob-Meyer decomposition of continuous submartingales. These results can be used to obtain an explicit expression of the constants appearing in the Burkholder-Davis-Gundy inequalities. A connection with some balayage formulae is also established.

Mots clés: Balayage; Burkholder-Davis-Gundy inequalities; Continuous Submartingales; Doob-Meyer decomposition

Domaines: Probabilités [math.PR]

Giovanni Peccati, Marc Yor. Burkholder's submartingales from a stochastic calculus perspective. 2007. ⟨hal-00149234⟩