2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230332In this monograph, we construct and study a sigma-finite measure on continuous functions from R_+ to R, strongly related to many probability measures obtained by penalisation of Brownian motion, i.e. as limits of probabilities which are absolutely continuous with respect to Wiener measure. This remarkable sigma-finite measure can be generalized in three other cases: one can start from a two-dimensional Brownian motion, from a recurrent diffusion with values in R_+, and from a discrete, recurrent Markov chain.Probability60G17; 60G40; 60G44; 60H10; 60J25; 60J60; 60J65text