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Lindley Processes With Correlated Changes, John Grant

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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 …