Radon-Nikodym derivatives, passages and maxima for a Gaussian process with particular covariance and mean
1975 ◽
Vol 12
(04)
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pp. 724-733
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Keyword(s):
We find expressions for the R–N derivative of the stationary Gaussian process with the particular covariance and mean, respectively, R(t, s) = max(1 – |t – s|, 0) and m(t)= aR(t, D), 0 ≦ D ≦ 1, within the time interval [0, 1]. We use these results, and a lemma on multiple reflections of the Wiener process, to find formulae for the probabilities of first passage time and maxima in [0, 1], and bounds on the former within [– 1, 1]. While previous work dealt extensively with the zero mean process, mean functions, as defined here, appear in signal detection and parameter estimation problems under the hypothesis that a rectangular signal centered at t = D is present in an observed process.
1976 ◽
Vol 13
(01)
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pp. 27-38
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2011 ◽
Vol 2011
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pp. 1-3
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1998 ◽
pp. 139-152
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Keyword(s):
1993 ◽
Vol 7
(1)
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pp. 125-148
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Keyword(s):
1986 ◽
pp. 113-116
Keyword(s):
1971 ◽
Vol 42
(3)
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pp. 946-951
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1961 ◽
Vol 32
(2)
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pp. 610-612
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