Geodesic
On the minimax detection of imperfectly known signal in a white Gaussian noise
Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 106-118 
M. V. Burnašev. On the minimax detection of imperfectly known signal in a white Gaussian noise. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 1, pp. 106-118. http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a7/
@article{TVP_1979_24_1_a7,
     author = {M. V. Burna\v{s}ev},
     title = {On the minimax detection of imperfectly known signal in a white {Gaussian} noise},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {106--118},
     year = {1979},
     volume = {24},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a7/}
}
TY  - JOUR
AU  - M. V. Burnašev
TI  - On the minimax detection of imperfectly known signal in a white Gaussian noise
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1979
SP  - 106
EP  - 118
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a7/
LA  - ru
ID  - TVP_1979_24_1_a7
ER  - 
%0 Journal Article
%A M. V. Burnašev
%T On the minimax detection of imperfectly known signal in a white Gaussian noise
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 106-118
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a7/
%G ru
%F TVP_1979_24_1_a7

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

Let according to the hypothesis $H_0$ the observed signal $X_t$ is given by the stochastic equation $$ dX_t=s_t dt+dW_t\qquad s_t\in S\subset L_2 [0, T], $$ where the set $S$ is known and $W_t$ is a Wiener process. Fot the alternative $H_1$ the observed signal $X_t$ is given by equation $dX_t=dW_t$. It is shown that very often instead of the set $S$ one can consider the reduced version of it. Nonasymptotic properties of maximum likelyhood ratio criteria are investigated.