Abstract:
For a Brownian motion B=(Bt)t⩽1 with B0=0, EBt=0, EB2t=t problems of probability distributions and their characteristics are considered for the variables
D=sup
where \sigma and \sigma' are times (non-Markov) of the absolute maximum and absolute minimum of the Brownian motion on [0,1] (i.e., B_\sigma=\sup_{0\le t\le 1}B_t, B_{\sigma'}=\inf_{0\le t'\le 1}B_{t'}).
Keywords:
Brownian motion, “downfalls” and “range”, Lévy theorem, Brownian meander.
Citation:
R. Douady, M. Yor, A. N. Shiryaev, “On probability characteristics of “downfalls” in a standard Brownian motion”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 3–13; Theory Probab. Appl., 44:1 (2000), 29–38
\Bibitem{DouYorShi99}
\by R.~Douady, M.~Yor, A.~N.~Shiryaev
\paper On probability characteristics of ``downfalls'' in a standard Brownian motion
\jour Teor. Veroyatnost. i Primenen.
\yr 1999
\vol 44
\issue 1
\pages 3--13
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\crossref{https://doi.org/10.4213/tvp594}
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\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 1
\pages 29--38
\crossref{https://doi.org/10.1137/S0040585X97977306}
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Linking options:
https://www.mathnet.ru/eng/tvp594
https://doi.org/10.4213/tvp594
https://www.mathnet.ru/eng/tvp/v44/i1/p3
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