Geodesic
Stochastic Processes as Curves in Hilbert Space
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 193-204

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

Regular complex-valued random processes $x(t)$ with finite moments of second order are studied by methods of Hilbert space geometry. A representation formula (4) is given for the process $x(t)$ in terms of “past and present innovations”. The number $N$ is called the complete spectral multiplicity of the process $x(t)$ and is the smallest number for which such a representation exists. It is shown that the multiplicity of $x(t)$ is uniquely determined by the corresponding correlation function and that one can always find a harmonizing process $x(t)$ which has the multiplicity prescribed in advance. 
@article{TVP_1964_9_2_a0,
     author = {Harald Cram\'er},
     title = {Stochastic {Processes} as {Curves} in {Hilbert} {Space}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {193--204},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1964},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a0/}
}
TY  - JOUR
AU  - Harald Cramér
TI  - Stochastic Processes as Curves in Hilbert Space
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1964
SP  - 193
EP  - 204
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a0/
LA  - en
ID  - TVP_1964_9_2_a0
ER  - 
%0 Journal Article
%A Harald Cramér
%T Stochastic Processes as Curves in Hilbert Space
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1964
%P 193-204
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a0/
%G en
%F TVP_1964_9_2_a0
Harald Cramér. Stochastic Processes as Curves in Hilbert Space. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 193-204. http://geodesic.mathdoc.fr/item/TVP_1964_9_2_a0/