Multiple Wiener integrals and stochastic integrals are defined for Gaussian processes, extending the related notions for the Wiener process. It is shown that every $L_2$-functional of a Gaussian process admits an adapted stochastic integral representation and an orthogonal series expansion in terms of multiple Wiener integrals. Also some results of Wiener's theory of nonlinear noise are generalized to noises other than white.
Publié le : 1978-08-14
Classification:
Gaussian processes,
multiple Wiener integrals,
nonlinear noise,
stochastic integrals,
iterated integrals,
adapted and future increments independent integrands,
60G15,
60H05,
60G10
@article{1176995480,
author = {Huang, Steel T. and Cambanis, Stamatis},
title = {Stochastic and Multiple Wiener Integrals for Gaussian Processes},
journal = {Ann. Probab.},
volume = {6},
number = {6},
year = {1978},
pages = { 585-614},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995480}
}
Huang, Steel T.; Cambanis, Stamatis. Stochastic and Multiple Wiener Integrals for Gaussian Processes. Ann. Probab., Tome 6 (1978) no. 6, pp. 585-614. http://gdmltest.u-ga.fr/item/1176995480/