Hausdorff–Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms
Alain Lucas, Emmanuel Thilly (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Displaying similar documents to “Local dimensions of the branching measure on a Galton–Watson tree”
Hausdorff–Besicovitch measure of fractal functional limit laws induced by Wiener process in Hölder norms
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The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly...
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On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Klaus Fleischmann, Vitali Wachtel (2009)
Annales de l'I.H.P. Probabilités et statistiques
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Under a well-known scaling, supercritical Galton–Watson processes converge to a non-degenerate non-negative random limit variable . We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent...