Let $F(c_0w)$ be a functional of the Wiener process with variance parameter $c^2_0$ and let $F(cw)$ be an extension of $F(c_0w)$ to $F(cw), c \in (0, c_0)$. Relations are derived between the Malliavin derivatives, between the derivatives with respect to the scale parameter $(\partial F(\rho cw)/\partial\rho)_{p = 1}$ and `noncoherent derivatives' such as $(dE(F(cw + \sqrt\varepsilon c\tilde{w}) \mid w)/d\varepsilon)_{\varepsilon = 0}$ where $\tilde{w}$ is another Wiener process independent of $w$ and between the generator of the nontime-homogeneous Ornstein-Uhlenbeck process.
Publié le : 1985-05-14
Classification:
Malliavin derivatives,
Malliavin calculus,
derivatives of Wiener functionals,
the infinite dimensional Ornstein-Uhlenbeck process,
60H99,
60J65
@article{1176993013,
author = {Zakai, Moshe},
title = {Malliavin Derivatives and Derivatives of Functionals of the Wiener Process with Respect to a Scale Parameter},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 609-615},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993013}
}
Zakai, Moshe. Malliavin Derivatives and Derivatives of Functionals of the Wiener Process with Respect to a Scale Parameter. Ann. Probab., Tome 13 (1985) no. 4, pp. 609-615. http://gdmltest.u-ga.fr/item/1176993013/