Une formule d'Itô pour les martingales continues à deux indices et quelques applications
type: Item
instance of: scholarly article
title: Une formule d'Itô pour les martingales continues à deux indices et quelques applications
zbMATH Open document ID: 0543.60062
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1984-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77235
review text: After having proved the existence of a continuous version of the quadratic variation of a two-parameter continuous martingale [On the quadratic variation of two-parameter continuous martingales. Ann. Probab. 12, 445-457 (1984)], the author provides in the paper under review an Itô differentiation formula for arbitrary two-parameter continuous martingales. Such a formula has already been obtained by \textit{L. Chevalier}, Bull. Sci. Math., II. Ser. 106, 19-62 (1982; Zbl 0493.60055), under the additional assumption that any square integrable martingale has a continuous version; in the presently more general setting the author proves this formula by a more accurate and ingenious application of martingales inequalities. As an application, the author proves the existence, continuity and regularity of the local time of these martingales with respect to a particular random measure (a quadratic variation related to the martingale). Finally a maximal inequality for stochastic integrals in one coordinate is presented.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 3864227
zbMATH Keywords: Itô differentiation formula
zbMATH Keywords: two-parameter continuous martingales
zbMATH Keywords: martingales inequalities
zbMATH Keywords: continuity and regularity of the local time
zbMATH Keywords: maximal inequality for stochastic integrals
author: David Nualart
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3864227