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Martingales and rates of presence in homogeneous fragmentations

Author

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  • Krell, N.
  • Rouault, A.

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)

Suggested Citation

  • Krell, N. & Rouault, A., 2011. "Martingales and rates of presence in homogeneous fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 135-154, January.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:1:p:135-154
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    References listed on IDEAS

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    1. Rouault, Alain, 1993. "Precise estimates of presence probabilities in the branching random walk," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 27-39, January.
    2. Hardy, Robert & Harris, Simon C., 2006. "A conceptual approach to a path result for branching Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1992-2013, December.
    3. Krell, Nathalie, 2008. "Multifractal spectra and precise rates of decay in homogeneous fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 897-916, June.
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