Graduate Thesis Or Dissertation
 

Branching Brownian Motion with One Absorbing and One Reflecting Boundary

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/n009w687g

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  • In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the utilityof such processes in modeling a biological population’s response to climate change. Webegin with a discussion of the beautiful theory that has been developed for such processeswithout boundaries, proceed through an adaptation of this theory to our finite setting withboundary conditions, and finally demonstrate a critical parameter value that answers thefundamental question of whether persistence is possible for our branching process, or ifextinction is inevitable. We also include a new and simple proof of Kesten’s persistencecriterion for branching Brownian motion with a single absorbing boundary. The bulk ofthe work is done by the distinguished path (or “spine”) analysis for branching processes.
  • Keywords: Branching Brownian motion, Climate Change, Mathematical Biology
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