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

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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https://hal.archives-ouvertes.fr/hal-01214773
Contributor : Sabine Mercier <>
Submitted on : Tuesday, October 13, 2015 - 9:29:20 AM
Last modification on : Friday, January 10, 2020 - 9:08:59 PM
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Agnès Lagnoux, Sabine Mercier, Pierre Vallois. Probability that the maximum of the reflected Brownian motion over a finite interval [0; t] is achieved by its last zero before t. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015, ⟨10.1214/ECP.vVOL-PID⟩. ⟨hal-01214773⟩

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