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Subject: renewal theory ×

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    Catalytic branching processes via spine techniques and renewal theory
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Döring, Leif; Roberts, Matthew I.
    In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number of particles in a variation of constants formulation. The long-time behavior is then deduced from renewal theorems and induction.
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    The longest excursion of a random interacting polymer
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Köcher, Janine; König, Wolfgang
    We consider a random N-step polymer under the influence of an attractive interaction with the origin and derive a limit law -- after suitable shifting and norming -- for the length of the longest excursion towards the Gumbel distribution. The embodied law of large numbers in particular implies that the longest excursion is of order log N long. The main tools are taken from extreme value theory and renewal theory.