Markov Chains with Asymptotically Zero Drift : Lamperti's Problem
Book Details
Format
Hardback or Cased Book
Book Series
New Mathematical Monographs
ISBN-10
1009554220
ISBN-13
9781009554220
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
May 8th, 2025
Print length
428 Pages
Product Classification:
Probability & statistics
Ksh 21,600.00
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This text provides a comprehensive presentation of results for time-homogeneous Markov chains with asymptotically zero drift. Including novel results and original research, this monograph will interest researchers and graduate students in probability, statistics and their applications.
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.
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