2015/07/06 by Andreas E. Kyprianou, Kyprianou, Andreas E., Thomas Madaule +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Branching (polymer chemistry) #Branching random walk #Brownian motion #Combinatorics #Discrete mathematics #Financial Risk and Volatility Modeling #Homogeneous #Martingale (probability theory) #Mathematical analysis #Mathematics #Multiplicative function #Physics #Random walk #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR
paper · pdf · doi:10.48550/arxiv.1507.01559
arxiv created 2015/07/06 · openalex publication_date 2015/07/06 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with non-negative displacements. Following recent developments in the theory of branching random walks, in particular the work of \citeAShi10, we consider the problem of the Seneta-Heyde norming of the so-called additive martingale at criticality. Aside from replicating results for branching random walks in the new setting of fragmentation processes, our main goal is to present a style of reasoning, based on Lp estimates, which works for a whole host of different branching-type processes. We show that our methods apply equally to the setting of branching random walks, branching Brownian motion as well as Gaussian multiplicative chaos.