2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75510In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to infinity, and we study the behaviour of this limit measure.ProbabilityAMS : 60B10, 60J65 (60G17, 60G44, 60J25, 60J55)text