We give a simple representation of two-parameter martingales in terms of a stochastic integral. This representation leads to the idea of the partial derivate of a martingale and to a generalization of the stochastic Green's theorem of the authors. Green's formula in this generalized form gives us a new and simpler proof of the fact that the derivative of a holomorphic process is holomorphic.
Publié le : 1977-08-14
Classification:
Stochastic integrals in the plane,
multiparameter martingales,
holomorphic processes,
60H05,
60G45
@article{1176995757,
author = {Cairoli, R. and Walsh, J. B.},
title = {Martingale Representations and Holomorphic Processes},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 511-521},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995757}
}
Cairoli, R.; Walsh, J. B. Martingale Representations and Holomorphic Processes. Ann. Probab., Tome 5 (1977) no. 6, pp. 511-521. http://gdmltest.u-ga.fr/item/1176995757/