  Previous work has established that the localized regime of wave transport in
open media is characterized by a position-dependent diffusion coefficient. In
this work we study how the concept of position-dependent diffusion affects the
delay time, the transverse confinement, the coherent backscattering, and the
time reversal of waves. Definitions of energy transport velocity of localized
waves are proposed. We start with a phenomenological model of radiative
transfer and then present a novel perturbational approach based on the
self-consistent theory of localization. The latter allows us to obtain results
relevant for realistic experiments in disordered quasi-1D wave guides and 3D
slabs.
