Probability that the maximum of the reflected Brownian motion over a finite interval [0; t] is achieved by its last zero before t - Archive ouverte HAL Access content directly
Journal Articles Electronic Communications in Probability Year : 2015

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

Agnès Lagnoux
Sabine Mercier

#### 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).

#### Domains

Mathematics [math] Statistics [math.ST]

### Dates and versions

hal-01214773 , version 1 (13-10-2015)

### Identifiers

• HAL Id : hal-01214773 , version 1
• ARXIV :
• DOI :

### Cite

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, 2015, ⟨10.1214/ECP.vVOL-PID⟩. ⟨hal-01214773⟩

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