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.

• | Author: Denis Denisov
• | Publisher: Cambridge University Press
• | Publication Date: May 08, 2025
• | Number of Pages: 00428 pages
• | Binding: Hardback or Cased Book
• | ISBN-10: 1009554220
• | ISBN-13: 9781009554220