Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Xin Liu

Committee Member

Robert Lund

Committee Member

Peter Kiessler

Committee Member

Brian Fralix


This dissertation studies a Lindley random walk model when the increment process driving the walk is strictly stationary. Lindley random walks govern customer waiting times in many queueing models and several natural and business processes, including snow depths, frozen soil depths, inventory quantities, etc. Probabilistic properties of a Lindley process with time-correlated stationary changes are explored. We provide a streamlined argument that the process admits a limiting stationary distribution when the mean of the incremental changes is negative and that the Lindley process is strictly stationary when starting from this stationary distribution. The Markov characteristics of the process are explored when the change process has a Markov structure of first or higher order. A derivation of the model's likelihood is given when the change process obeys a pth order autoregression. Due to the unwieldy nature of this likelihood, a particle filtering method of evaluating and optimizing it is devised and studied via simulation.



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