This text examines Markov chains whose drift tends to zero at infinity, a topic
sometimes referred to as Lamperti’s problem. It can be considered a subcategory of random walks, which are helpful in studying stochastic models such as 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 chain 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.