Stochastic integrals of anticipating processes and dual predictable projections.

Catherine Donati-Martin; Marc Yor

Publicacions Matemàtiques (1999)

  • Volume: 43, Issue: 1, page 281-301
  • ISSN: 0214-1493

Abstract

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We define a stochastic anticipating integral δμ with respect to Brownian motion, associated to a non adapted increasing process (μt), with dual projection t. The integral δμ(u) of an anticipating process (ut) satisfies: for every bounded predictable process ft,E [ (∫ fsdBs ) δμ(u) ] = E [ ∫ fsusdμs ].We characterize this integral when μt = supt ≤s ≤ 1 Bs. The proof relies on a path decomposition of Brownian motion up to time 1.

How to cite

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Donati-Martin, Catherine, and Yor, Marc. "Intégrales stochastiques de processus anticipants et projections duales prévisibles.." Publicacions Matemàtiques 43.1 (1999): 281-301. <http://eudml.org/doc/41359>.

@article{Donati1999,
author = {Donati-Martin, Catherine, Yor, Marc},
journal = {Publicacions Matemàtiques},
keywords = {Proceso de difusión; Integración estocástica; Ecuaciones diferenciales estocásticas; Procesos estocásticos; Movimiento browniano; stochastic anticipating integral; dual projection; path decomposition; balayage formula},
language = {fre},
number = {1},
pages = {281-301},
title = {Intégrales stochastiques de processus anticipants et projections duales prévisibles.},
url = {http://eudml.org/doc/41359},
volume = {43},
year = {1999},
}

TY - JOUR
AU - Donati-Martin, Catherine
AU - Yor, Marc
TI - Intégrales stochastiques de processus anticipants et projections duales prévisibles.
JO - Publicacions Matemàtiques
PY - 1999
VL - 43
IS - 1
SP - 281
EP - 301
LA - fre
KW - Proceso de difusión; Integración estocástica; Ecuaciones diferenciales estocásticas; Procesos estocásticos; Movimiento browniano; stochastic anticipating integral; dual projection; path decomposition; balayage formula
UR - http://eudml.org/doc/41359
ER -

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