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It is shown that in detecting sequentially a deterministic signal $ psi(t) $ in white noise $ eta(t) $ a similar identity (iii) in theorem 2.1, to the Wald's holds concerning a stopping time $ \tau $ ...determined by making use of a likelihood ratio. It is also shown that $ \tau $ has finite moments of any order under quite weak conditions over the signal. The exact A. S. N. $ E{\tau} $ in a constant signal case has been obtained and given by (2, 8). It is also considered a detection problem of a constant signal $ psi(t) equiv alpha $ in a coloured noise based on a sub-optimal statistic which become optimal when the noise were white. Similar properties of a stopping time $ \tau $ to those in the white noise case have been obtained in theorem 3.1.show more
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