2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135410We show that the slopes between h-extrema of the drifted 1D Brownian motion form a stationary alternating marked point process, extending the result of J. Neveu and J. Pitman for the non drifted case. Our analysis covers the results on the statistics of h-extrema obtained by P. Le Doussal, C. Monthus and D. Fisher via a Renormalization Group analysis and gives a complete description of the slope between h-extrema covering the origin by means of the Palm--Khinchin theory. Moreover, we analyze the behavior of the Brownian motion near its h-extrema.28 pages, 4 figuresProbabilityMathematical Physics60J65, 60G55text