Denis Denisov, Dmitry Korshunov, Vitali Wachtel

Markov Chains with Asymptotically Zero Drift

Lamperti's Problem

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 432
• Erscheinungstermin: 30. Juni 2025
• Englisch
• ISBN-13: 9781009554220
• ISBN-10: 1009554220
• Artikelnr.: 73333632

Autorenporträt

Denis Denisov is Reader in Probability in the Department of Mathematics at the University of Manchester. His research interests include multidimensional random walks, ordered and conditioned random walks, Markov chains and diffusion processes.

Inhaltsangabe

1. Introduction
2. Lyapunov functions and classification of Markov chains
3. Down-crossing probabilities for transient Markov chain
4. Limit theorems for transient and null-recurrent Markov chains with drift proportional to 1/x
5. Limit theorems for transient Markov chains with drift decreasing slower than 1/x
6. Asymptotics for renewal measure for transient Markov chain via martingale approach
7. Doob's h-transform: transition from recurrent to transient chain and vice versa
8. Tail analysis for recurrent Markov chains with drift proportional to 1/x
9. Tail analysis for positive recurrent Markov chains with drift going to zero slower than 1/x
10. Markov chains with asymptotically non-zero drift in Cramér's case
11. Applications.