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August, 1984 Randomly Started Signals with White Noise
Burgess Davis, Itrel Monroe
Ann. Probab. 12(3): 922-925 (August, 1984). DOI: 10.1214/aop/1176993243

Abstract

It is shown that if $B(t), t \geq 0$, is a Wiener process, $U$ is an independent random variable uniformly distributed on (0, 1), and $\varepsilon$ is a constant, then the distribution of $B(t) + \varepsilon \sqrt{(t - U)^+}, 0 \leq t \leq 1$, is absolutely continuous with respect to Wiener measure on $C\lbrack 0, 1\rbrack$ if $0 < \varepsilon < 2$, and singular with respect to this measure if $\varepsilon > \sqrt 8$.

Citation

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Burgess Davis. Itrel Monroe. "Randomly Started Signals with White Noise." Ann. Probab. 12 (3) 922 - 925, August, 1984. https://doi.org/10.1214/aop/1176993243

Information

Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0599.60041
MathSciNet: MR744249
Digital Object Identifier: 10.1214/aop/1176993243

Subjects:
Primary: 60J65
Secondary: 60G17 , 60G30

Keywords: Brownian motion paths

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • August, 1984
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