  We 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.
