We analyze and identify stationary fields with linear regressions
and quadratic conditional variances. We give sufficient conditions to determine
one-dimensional distributions uniquely as normal and as certain compactly
supported distributions. Our technique relies on orthogonal polynomials, which
under our assumptions turn out to be a version of the so-called continuous
q-Hermite polynomials.
Publié le : 2001-02-14
Classification:
Conditional moments,
hypergeometric orthogonal polynomials,
q-Hermite polynomials,
q -Gaussian processes,
linear regression,
60E99,
60G10
@article{1008956342,
author = {Bryc, W\l odzimierz},
title = {Stationary random fields with linear regressions},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 504-519},
language = {en},
url = {http://dml.mathdoc.fr/item/1008956342}
}
Bryc, Włodzimierz. Stationary random fields with linear regressions. Ann. Probab., Tome 29 (2001) no. 1, pp. 504-519. http://gdmltest.u-ga.fr/item/1008956342/