  We define a large class of multifractal random measures and processes with
arbitrary log-infinitely divisible exact or asymptotic scaling law. These
processes generalize within a unified framework both the recently defined
log-normal "Multifractal Random Walk" processes (MRW) and the log-Poisson
"product of cynlindrical pulses". Their construction involves some ``continuous
stochastic multiplication'' from coarse to fine scales. They are obtained as
limit processes when the finest scale goes to zero. We prove the existence of
these limits and we study their main statistical properties including non
degeneracy, convergence of the moments and multifractal scaling.
