Markov Chains with Asymptotically Zero Drift

By: Denis Denisov, Dmitry Korshunov, Vitali Wachtel

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Hardcover | 8 May 2025

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Hardcover
430 Pages

Dimensions(cm)
22.86 x 15.24 x 2.39

Hardcover

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This text examines Markov chains whose drift tends to zero at infinity, a topic sometimes labelled as 'Lamperti's problem'. It can be considered a subcategory of random walks, which are helpful in studying stochastic models like branching processes and queueing systems. Drawing on Doob's h-transform and other tools, the authors present novel results and techniques, including a change-of-measure technique for near-critical Markov chains. The final chapter presents a range of applications where these special types of Markov chains occur naturally, featuring a new risk process with surplus-dependent premium rate. This will be a valuable resource for researchers and graduate students working in probability theory and stochastic processes.

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