On the excursions of drifted Brownian motion and the successive passage times of Brownian motion

Abstract

By using the law of the excursions of Brownian motion with drift, we find the distribution of the $n-$th passage time of Brownian motion through a straight line $S(t)=a+bt.$ In the special case when $b=0,$ we extend the result to a space-time transformation of Brownian motion.

4 figures, accepted for publication in Physica A

References in corpus (2)

• On the first-passage time of an integrated Gauss-Markov process
• On the representation of an integrated Gauss-Markov process

Cited by in corpus (1)

• The joint distributions of running maximum of a Slepian processes