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Markov Chains with Asymptotically Zero Drift
Denis DenisovDmitry KorshunovVitali Wachtel
其他書名
Lamperti's Problem
出版Cambridge University Press, 2025-05-08
主題Mathematics / Probability & Statistics / General
ISBN10095542209781009554220
URLhttp://books.google.com.hk/books?id=CS4F0QEACAAJ&hl=&source=gbs_api
註釋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.