Geodesic
Conditions for moments of the number of zeroes of Gaussian stationary processes to be finite
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 631-641 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We deal with factorial moments $N_m(t)$ of the number of zeroes of a Gaussian stationary process $\xi_{\tau}$, $\mathbf M\xi_{\tau}=0$, $\tau\in[0,t]$. For $\xi_t$ having the property of local non-determinism of order $k$ (Definition 1), necessary and sufficient conditions for moments $N_m(t)$ to be finite are obtained (Theorems 1 and 2). In Theorems 3 and 4 these conditions are simplified for the case $k=1$. 
@article{TVP_1977_22_3_a19,
     author = {R. N. Miro\v{s}in},
     title = {Conditions for moments of the number of zeroes of {Gaussian} stationary processes to be finite},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {631--641},
     year = {1977},
     volume = {22},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a19/}
}
TY  - JOUR
AU  - R. N. Mirošin
TI  - Conditions for moments of the number of zeroes of Gaussian stationary processes to be finite
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1977
SP  - 631
EP  - 641
VL  - 22
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a19/
LA  - ru
ID  - TVP_1977_22_3_a19
ER  - 
%0 Journal Article
%A R. N. Mirošin
%T Conditions for moments of the number of zeroes of Gaussian stationary processes to be finite
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1977
%P 631-641
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a19/
%G ru
%F TVP_1977_22_3_a19
R. N. Mirošin. Conditions for moments of the number of zeroes of Gaussian stationary processes to be finite. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 631-641. http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a19/