The asymptotic behavior of fragmentation processes
The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate their pathwise asymptotic behavior as . In the so-called homogeneous case, we first point at a law of large numbers and a central limit theorem for (a modified version of) the empirical distribution of the fragments at time . These results are reminiscent of those of Asmussen and Kaplan [3] and Biggins...