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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.
Reviewer: L.Paditz

MSC:

62F05 Asymptotic properties of parametric tests
94A40 Channel models (including quantum) in information and communication theory
60G35 Signal detection and filtering (aspects of stochastic processes)

Citations:

Zbl 0664.00021
Full Text: EuDML