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Hyper-finite methods for multi-dimensional stochastic processes

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Title: Hyper-finite methods for multi-dimensional stochastic processes
Author: Reimers, Mark Allan
Degree Doctor of Philosophy - PhD
Program Mathematics
Copyright Date: 1986
Subject Keywords Finite differences; Stochastic processes
Abstract: In this thesis we introduce Non-Standard Methods, in particular the use of hyperfinite difference equations, to the study of space-time random processes. We obtain a new existence theorem in the spirit of Keisler (1984) for the one dimensional heat equation forced non-linearly by white noise. We obtain several new results on the sample path properties of the Critical Branching Measure Diffusion, and show that in one dimension it has a density which satisfies a non-linearly forced heat equation. We also obtain results on the dimension of the support of the Fleming-Viot Process.
URI: http://hdl.handle.net/2429/27515
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

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