Local additive functionals of Gaussian random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 32-44
Local additive functional $\Xi$ is a random finite-additive measure whose value on the parallelepiped $V\subset R^\nu$ belongs to the $\sigma$-algebra $\mathfrak B_V$ generated by the values of generalized Gaussian random field $\zeta=\{\zeta(\varphi),\varphi\in\mathfrak Y(R^\nu)\}$ on $V$. This functional are described in terms of their representation as multiple stochastic Wiener–Ito integrals.
@article{TVP_1983_28_1_a1,
author = {R. L. Dobru\v{s}in and M. Ya. Kel'bert},
title = {Local additive functionals of {Gaussian} random fields},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {32--44},
year = {1983},
volume = {28},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a1/}
}
R. L. Dobrušin; M. Ya. Kel'bert. Local additive functionals of Gaussian random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 32-44. http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a1/