Let $T$ be the set of vertices of a homogeneous tree and let $(X_t)_{t\in T}$ be a second-order real or complex-valued process such that the expected value $\mathbb{E}(X_s\bar{X}_t)$ depends only on the distance between the vertices $s$ and $t$. In this paper we construct a measure space $(K, \mathscr{H}, m)$ and an isometry of the closed subspace of $L^2_\mathbb{C}(\Omega, \mathscr{A}, P)$ spanned by $(X_t)_{t\in T}$ onto $L^2(m)$.
Publié le : 1994-01-14
Classification:
Stationary processes,
time series,
symmetric spaces,
Gelfand pairs,
homogeneous trees,
Cartier-Dunau polynomials,
60G10,
60G15,
60B99
@article{1176988856,
author = {Arnaud, Jean-Pierre},
title = {Stationary Processes Indexed by a Homogeneous Tree},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 195-218},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988856}
}
Arnaud, Jean-Pierre. Stationary Processes Indexed by a Homogeneous Tree. Ann. Probab., Tome 22 (1994) no. 4, pp. 195-218. http://gdmltest.u-ga.fr/item/1176988856/