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Small-time asymptotics of coalescent and Fleming-Viot processes
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Hanson, Philip A. (2022) Small-time asymptotics of coalescent and Fleming-Viot processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3821608
Abstract
Measure-valued and coalescent processes have a long and rich history in the field of population genetics. Through duality, these processes are intimately linked and the study of one often leads to insights in the other. In this thesis we investigate the small-time behaviour of backwards-in-time genealogical processes to establish a diffusion limit at t = 0. Forwards in time we consider linear combinations of an i.i.d. collection of Fleming-Viot processes, describing LLN and CLT style limits. In order to establish convergence in the second chapter, we require tightness. The duality of these processes and results from our first chapter are essential in proving this and much of the second chapter.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes, Coalescing, Genealogy, Poisson processes, Central limit theorem | ||||
Official Date: | February 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Spanó, Dario ; Jenkins, Paul A. ; Koskela, Jere | ||||
Sponsors: | University of Warwick. Department of Statistics ; Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | vi, 119 leaves | ||||
Language: | eng |
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