Markov Chains with Asymptotically Zero Drift

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.