Martingales and rates of presence in homogeneous fragmentations

N. Krell and A. Rouault

Stochastic Processes and their Applications, 2011, vol. 121, issue 1, 135-154

Abstract: The main focus of this work is the asymptotic behavior of mass-conservative homogeneous fragmentations. Considering the logarithm of masses makes the situation reminiscent of branching random walks. The standard approach is to study asymptotical exponential rates (Berestycki (2003)Â [3], Bertoin and Rouault (2005)Â [12]). For fixed v>0, either the number of fragments whose sizes at time t are of order is exponentially growing with rate C(v)>0, i.e. the rate is effective, or the probability of the presence of such fragments is exponentially decreasing with rate C(v)

Keywords: Fragmentation; Lévy; process; Martingales; Probability; tilting (search for similar items in EconPapers)
Date: 2011
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