Fine properties of symbiotic branching processes

Döring, Leif

URN: urn:nbn:de:kobv:83-opus-23653
Document Type: Doctoral dissertation
Year of publication: 2009
Place of publication: Berlin
University: Technische Universität Berlin
Evaluator: Blath, Jochen
Date of oral examination: 23 September 2009
Publication language: English
Institution: School of Business Informatics and Mathematics > Stochastik (Döring 2017-)
Subject: 510 Mathematics
Subject headings (SWD): Mathematik
Individual keywords (German): Ausbreitungsgeschwindigkeite , Konvergenz in Verteilung , Momente , Stochastische Prozesse , Verzweigung
Keywords (English): Branching , Convergence in Law , Moments , Stochastic Processes , Wavespeed
Abstract: In this work we introduce a critical curve separating the asymptotic behaviour of the moments of the symbiotic branching model, introduced by Etheridge and Fleischmann \cite{EF04}, into two regimes. Using arguments based on two different dualities and a classical result of Spitzer \cite{S58} on the exit-time of a planar Brownian motion from a wedge, we prove that the parameter governing the model provides regimes of bounded and exponentially fast growing higher moments separated by subexponential growth. The moments turn out to be closely linked to the limiting distribution as time tends to infinity. The limiting distribution can be derived by a self-duality argument extending a result of Dawson and Perkins \cite{DP98} for the mutually catalytic branching model. As an application, we show how a bound on the $18$th moment improves the result of \cite{EF04} on the speed of the interface of the symbiotic branching model.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.

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Döring, Leif ORCID: 0000-0002-4569-5083 (2009) Fine properties of symbiotic branching processes. Berlin [Doctoral dissertation]

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