Stochastic calculus with anticipating integrands
type: Item
instance of: scholarly article
title: Stochastic calculus with anticipating integrands
zbMATH Open document ID: 0629.60061
DOI: 10.1007/BF00353876
publication date: 1988-01-01T00:00:00Z
review text: We study the stochastic integral defined by \textit{A. V. Skorohod} in Teor. Veroyatn. Primen. 20, 223-238 (1975; Zbl 0333.60060) of a possibly anticipating integrand, as a function of its upper limit, and establish an extended Itô formula. We also introduce an extension of Stratonovich's integral, and establish the associated chain rule. In all the results, the adaptedness of the integrand is replaced by a certain smoothness requirement.
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 4024434
zbMATH Keywords: anticipating integrand
zbMATH Keywords: extended Itô formula
zbMATH Keywords: extension of Stratonovich's integral
author: David Nualart
author: Etienne Pardoux
MaRDI profile type: Publication
Wikidata QID: Q96624319
cites work: An extension of the stochastic integral
cites work: Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions
cites work: L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel
cites work: Q3959169
cites work: Q3336456
cites work: Multiple Wiener integral
cites work: On backward stochastic differential equations
cites work: White noise approach to stochastic integration
cites work: Propriété de trace en dimension infinie d'espaces du type Sobolev
cites work: Q3771353
cites work: Generalized stochastic integrals and the Malliavin calculus
cites work: Malliavin's calculus and stochastic integral representations of functional of diffusion processes†
cites work: Quelques propriétés de l’intégrale stochastique du type noncausal
cites work: A two-sided stochastic integral and its calculus
cites work: On stochastic integration by series of Wiener integrals
cites work: Q3706261
cites work: Derivatives of Wiener functionals and absolute continuity of induced measures
cites work: On a Generalization of a Stochastic Integral
cites work: The Malliavin calculus
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4024434