Markov chains with asymptotically zero drift : Lamperti's problem / Denis Denisov, Dmitry Korshunov, Vitali Wachtel .

Format:

Book

Author/Creator:

Denisov, Denis, author.

Korshunov, Dmitry, 1966- author.

Wachtel, Vitali, author.

Series:

New mathematical monographs ; 51.

New mathematical monographs ; 51

Language:

English

Subjects (All):

Random walks (Mathematics).

Asymptotic distribution (Probability theory).

Markov processes.

Physical Description:

1 online resource (xv, 412 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2025.

Summary:

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.

Notes:

Title from publisher's bibliographic system (viewed on 24 Apr 2025).

Includes bibliographical references and index.

ISBN:

1-009-55421-2

9781009554213

1-009-55423-9