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Probability that the maximum of the reflected Brownian motion over a finite interval [0; t] is achieved by its last zero before t

Authors
  • Lagnoux, Agnès
  • Mercier, Sabine
  • Vallois, Pierre
Publication Date
Sep 08, 2015
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
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Abstract

Probability that the maximum of the reflected Brownian motion over a finite interval [0, t] is achieved by its last zero before t Abstract We calculate the probability pc that the maximum of a reflected Brownian motion U is achieved on a complete excursion, i.e. pc := P U (t) = U * (t) where U (t) (respectively U * (t)) is the maximum of the process U over the time interval [0, t] (resp. 0, g(t) where g(t) is the last zero of U before t).

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