  For three constrained Brownian motions, the excursion, the meander, and the
reflected bridge, the densities of the maximum and of the time to reach it were
expressed as double series by Majumdar, Randon-Furling, Kearney, and Yor
(2008). Some of these series were regularized by Abel summation. Similar
results for Bessel processes were obtained by Schehr and Le Doussal (2010)
using the real space renormalization group method. Here this work is reviewed,
and extended from the point of view of one-dimensional diffusion theory to some
other diffusion processes including skew Brownian bridges and generalized
Bessel meanders. We discuss the limits of the application of this method for
other diffusion processes.
