  Log-normal continuous random cascades form a class of multifractal processes
that has already been successfully used in various fields. Several statistical
issues related to this model are studied. We first make a quick but extensive
review of their main properties and show that most of these properties can be
analytically studied. We then develop an approximation theory of these
processes in the limit of small intermittency $\lambda^2\ll 1$, i.e., when the
degree of multifractality is small. This allows us to prove that the
probability distributions associated with these processes possess some very
simple aggregation properties accross time scales. Such a control of the
process properties at different time scales, allows us to address the problem
of parameter estimation. We show that one has to distinguish two different
asymptotic regimes: the first one, referred to as the ''low frequency regime'',
corresponds to taking a sample whose overall size increases whereas the second
one, referred to as the ''high frequency regime'', corresponds to sampling the
process at an increasing sampling rate. We show that, the first regime leads to
convergent estimators whereas, in the high frequency regime, the situation is
much more intricate : only the intermittency coefficient $\lambda^2$ can be
estimated using a consistent estimator. However, we show that, in practical
situations, one can detect the nature of the asymptotic regime (low frequency
versus high frequency) and consequently decide whether the estimations of the
other parameters are reliable or not. We finally illustrate how both our
results on parameter estimation and on aggregation properties, allow one to
successfully use these models for modelization and prediction of financial time
series.
