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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 3, Pages 544–554
(Mi tvp2197)
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This article is cited in 15 scientific papers (total in 15 papers)
On the sequential hypotheses testing for signals in white Gaussian noise
G. K. Golubev, R. Z. Has'minskiĭ Moscow
Abstract:
The problem of the sequential testing of hypotheses $H_i$, $i=1,\dots,N$, where hypotheses $H_i$ are described by the observed process (1.1), is considered. Let the assumption (1.3) be fulfilled and let $\pi_i(t)$ be defined by the formula (2.3), where $P_i(\,\cdot\,)$ is the measure corresponding to the observed
process (1.1). It is proved that the decision rule (2.4) guarantees the asymptotically minimum expectation of time $\tau_\alpha^*$ of making the decision, if the probability of error $\alpha$ tends to zero. It is proved also that this optimal expectation of $\tau_\alpha^*$ satisfies the equation (2.6). It is found that the asymptotically optimal decision rule supplies the gain approximately in $4^\lambda$ times in comparison with the best nonsequential decision rule if $\alpha\ll 1$.
Received: 06.05.1980
Citation:
G. K. Golubev, R. Z. Has'minskiǐ, “On the sequential hypotheses testing for signals in white Gaussian noise”, Teor. Veroyatnost. i Primenen., 28:3 (1983), 544–554; Theory Probab. Appl., 28:3 (1984), 573–584
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https://www.mathnet.ru/eng/tvp2197 https://www.mathnet.ru/eng/tvp/v28/i3/p544
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