## Asymptotic solution of a problem of search for a signal in a multichannel system.(Russian)Zbl 0712.62017

Mat. Issled. 109, 15-35 (1989).
[For the entire collection see Zbl 0664.00021.]
Consider a system with k $$(k>1)$$ channels, where the observed output of the i-th channel is a random process $$X^ i=\{X^ i_ t\}$$, e.g. a Wiener process, $$t\in R^+$$ or $$t\in Z^+$$. Assume that these processes are independent. Let the distribution of $$X^ i$$ depend on an unknown parameter $$\vartheta_ i$$, where $$\vartheta_ i\in \{\mu_ 0,\mu_ 1\}$$; $$\vartheta_ i=\mu_ 0$$ means that the considered signal does not appear in the i-th channel and $$\vartheta_ i=\mu_ 1$$ means the other case, respectively.
Two extreme situations are possible: to analyse only one channel or simultaneously all channels, respectively. A further problem consists in the control of the observation process. The aim of this paper consists in the construction of a statistical test to check the hypothesis $$H_ i:\vartheta_ i=\mu_ 1$$, $$\vartheta_ j=\mu_ 0$$, $$\forall j\neq i$$, or $$H_ 0:\vartheta_ j=\mu_ 0$$, $$\forall j$$ (the signal is missing in the system) and in the proof of an asymptotical optimality criterion.