We consider waves propagating in a randomly layered medium with long-range
correlations. An example of such a medium is studied in \citeMS and leads, in
particular, to an asymptotic travel time described in terms of a fractional
Brownian motion. Here we study the asymptotic transmitted pulse under very
general assumptions on the long-range correlations. In the framework that we
introduce in this paper, we prove in particular that the asymptotic time-shift
can be described in terms of non-Gaussian and/or multifractal processes.Comment: Published in at http://dx.doi.org/10.1214/10-AAP689 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
