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

2015/05/13 by Agnès Lagnoux, Lagnoux, Agnès, Sabine Mercier +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1505.03274

9 pages ; 1 figure

arxiv created 2015/05/13 · arxiv updated 2015/05/14

Abstract

We calculate the probability p_c that the maximum of a reflected Brownian motion U is achieved on a complete excursion, i.e. p_c:=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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