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

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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. 
@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},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_1_a7/}
}
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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/