Randomly Started Signals with White Noise
Davis, Burgess ; Monroe, Itrel
Ann. Probab., Tome 12 (1984) no. 4, p. 922-925 / Harvested from Project Euclid
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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 $\varepsilon > \sqrt 8$.
Publié le : 1984-08-14
Classification:  Brownian motion paths,  60J65,  60G30,  60G17 
@article{1176993243,
     author = {Davis, Burgess and Monroe, Itrel},
     title = {Randomly Started Signals with White Noise},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 922-925},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993243}
}

Davis, Burgess; Monroe, Itrel. Randomly Started Signals with White Noise. Ann. Probab., Tome 12 (1984) no. 4, pp.  922-925. http://gdmltest.u-ga.fr/item/1176993243/