DOIAbstract
AbstractIn the present paper we compute the laws of some functionals of doubly perturbed Brownian motion, which is the solution of the equation Xt=Bt+αsups⩽tXs+βinfs⩽tXs, where α,β<1, and B is a real Brownian motion. We first show that the process obtained by juxtaposing the positive (resp. negative) excursions of this solution depends only on α (resp. β). Moreover, these two processes are independent. As a consequence of this splitting we compute, by direct calculations, the law of the occupation time in [0,∞) and we specify the joint distribution of the time and position at which doubly perturbed Brownian motion exits an interval
Add to ORKG