Strong convergence to diffusion processes with application to queueing theory
Amir, Abdelmadjid
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Permalink
https://hdl.handle.net/2142/19184
Description
Title
Strong convergence to diffusion processes with application to queueing theory
Author(s)
Amir, Abdelmadjid
Issue Date
1990
Doctoral Committee Chair(s)
Philipp, Walter
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Statistics
Language
eng
Abstract
We show the almost sure uniform pathwise convergence of birth and death processes and random walks to Brownian motion with drift and sticky Brownian motion. We thus provide constructive definitions of such diffusions. In the first case we give a queueing application and in the latter case we provide the transition distribution of the sticky Brownian motion along with its local variations at zero and a law of the iterated logarithm.
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