Geodesic
On the problem of detecting random trajectories
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 669-680

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A consistent test is constructed for the hypothesis that there is a particle which performs random walk along the integer lattice of the real line and carries a “useful signal” in the presence of “noise”. The limiting form of the linear approximation to the likelihood ratio is found to be a convolution of the standard normal distribution and a functional of the standard Wiener process.
Keywords: likelihood ratio statistics, random walk, signal detection in the presence of noise, functional of a Wiener process, problem of detection of random trajectories. 
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     author = {I. M. Arbekov and V. I. Vinokurov and B. V. Ryazanov},
     title = {On the problem of detecting random trajectories},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {669--680},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a1/}
}
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I. M. Arbekov; V. I. Vinokurov; B. V. Ryazanov. On the problem of detecting random trajectories. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 669-680. http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a1/