An anticipating stochastic integral is proposed for 'normal martingales'. It agrees with the Skorohod integral in the Brownian case. A variational derivative of Malliavin type is also defined. An integration by parts formula is given which has some subtle and important differences from the formula in the Brownian case. The existence and uniqueness of solutions of linear stochastic differential equations with anticipating exogenous driving terms are also established.
Publié le : 1998-03-14
Classification:
anticipating stochastic differential equation,
anticipating stochastic integral,
Azéma's martingale,
homogeneous chaos,
multiple stochastic integral,
normal martingales,
stochastic integration by parts,
structure equation,
variational derivative
@article{1175865491,
author = {Ma, Jin and Protter, Philip and San Mart\'\i in, Jaime},
title = {Anticipating integrals for a class of martingales},
journal = {Bernoulli},
volume = {4},
number = {1},
year = {1998},
pages = { 81-114},
language = {en},
url = {http://dml.mathdoc.fr/item/1175865491}
}
Ma, Jin; Protter, Philip; San Martíin, Jaime. Anticipating integrals for a class of martingales. Bernoulli, Tome 4 (1998) no. 1, pp. 81-114. http://gdmltest.u-ga.fr/item/1175865491/