A stochastic calculus for continuous N-parameter strong martingales
type: Item
instance of: scholarly article
title: A stochastic calculus for continuous N-parameter strong martingales
zbMATH Open document ID: 0652.60056
DOI: 10.1016/0304-4149(85)90015-8
author: P. Imkeller
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale with respect to an increasing family of \(\sigma\)-fields satisfying the conditional independence property introduced by \textit{R. Cairoli} and \textit{J. B. Walsh}, Acta Math. 134, 111-183 (1975; Zbl 0334.60026). A stochastic calculus for multiparameter martingales is developed, and several Itô-type stochastic differentiation formulas are established. One of them is in terms of some stochastic measures or ``variations'' associated with M, another is obtained by decomposing these measures and a third one is derived from the second by iterated application of a stochastic version of Green's formula. These results are based on the multiparameter Burkholder L p-inequalities and the Itô formula derived by \textit{M. F. Allain}, Z. Wahrscheinlichkeitstheor. Verw. Gebiete 65, 421-444 (1984; Zbl 0534.60044).
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4064176
zbMATH Keywords: N-parameter strong martingale
zbMATH Keywords: stochastic calculus for multiparameter martingales
zbMATH Keywords: stochastic version of Green's formula
zbMATH Keywords: multiparameter Burkholder L p-inequalities
zbMATH Keywords: Itô formula
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90015-8
OpenAlex ID: W2054031282
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description: scientific article; zbMATH DE number 4064176