Abstract:
The testing of two hypotheses in Gaussian noise is considered, namely, of the hypothesis $H_0$ that there is no particle in the observation field, and of the hypothesis $H_1$ of presence of a particle in the field, with the distribution of the paths of the particle being known. An upper bound is obtained for signal-to-noise ratios for which it is impossible in principle to test the hypotheses with arbitrarily small error probabilities, and a lower bound is obtained for signal-to-noise ratios for which this is possible.
Fulltext:
PDF file (1050 kB)