Geodesic
Convergence of a canonical expansion for normal fields
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 565-572 
E. I. Ostrovskii. Convergence of a canonical expansion for normal fields. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 565-572. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/
@article{MZM_1973_14_4_a14,
     author = {E. I. Ostrovskii},
     title = {Convergence of a~canonical expansion for normal fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--572},
     year = {1973},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/}
}
TY  - JOUR
AU  - E. I. Ostrovskii
TI  - Convergence of a canonical expansion for normal fields
JO  - Matematičeskie zametki
PY  - 1973
SP  - 565
EP  - 572
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/
LA  - ru
ID  - MZM_1973_14_4_a14
ER  - 
%0 Journal Article
%A E. I. Ostrovskii
%T Convergence of a canonical expansion for normal fields
%J Matematičeskie zametki
%D 1973
%P 565-572
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a14/
%G ru
%F MZM_1973_14_4_a14

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present study we consider a normal separable stochastic continuous field, and we prove the convergence of a Karhunen series with probability 1 for all parameter values. This leads in particular, to the nonrandomness of points of the discontinuity and values of the discontinuity. A criterion is presented for the convergence of the canonical expansion in a uniform norm.