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Published online by Cambridge University Press: 24 April 2025
Chapters 4 and 5 of the present monograph deal comprehensively with limit theorems for transient Markov chains. In Chapter 4 we consider drifts of order 1/x, and prove limit theorems including convergence to a Γ-distribution and functional convergence to a Bessel process. We also study the asymptotic behaviour of the renewal measure, which is not straightforward as there is no law of large numbers owing to the comparable contributions of the drift and fluctuations.
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