Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 481-490
Citer cet article
R. N. Miroshin. A sufficient condition for the number of zeros of a differentiable Gaussian stationary process to be finite. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 3, pp. 481-490. http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a3/
@article{TVP_1973_18_3_a3,
author = {R. N. Miroshin},
title = {A sufficient condition for the number of zeros of a differentiable {Gaussian} stationary process to be finite},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {481--490},
year = {1973},
volume = {18},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a3/}
}
TY - JOUR
AU - R. N. Miroshin
TI - A sufficient condition for the number of zeros of a differentiable Gaussian stationary process to be finite
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1973
SP - 481
EP - 490
VL - 18
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a3/
LA - ru
ID - TVP_1973_18_3_a3
ER -
%0 Journal Article
%A R. N. Miroshin
%T A sufficient condition for the number of zeros of a differentiable Gaussian stationary process to be finite
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1973
%P 481-490
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1973_18_3_a3/
%G ru
%F TVP_1973_18_3_a3
We are concerned with factorial moments $N_m(T)$ of the number of zeros of a Gaussian stationary process $\xi_t$, $\mathbf M\xi_t=0$, $t\in[0,T]$. For $\xi_t$ having the derivative $\xi'_t$, a sufficient condition for moments $N_m(T)$ to be finite is obtained (Theorem 1). In theorems 2 and 3 we deal with applications of Theorem 1 to concrete classes of $\xi_t$.
