Markov Chains with Asymptotically Zero Drift
Markov Chains with Asymptotically Zero Drift: Lamperti's Problem
English | 2025 | ISBN: 1009554220 | 429 Pages | PDF | 2.4 MB
English | 2025 | ISBN: 1009554220 | 429 Pages | PDF | 2.4 MB
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.