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Markov chains with asymptotically zero drift: Lamperti's problem

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Markov chains with asymptotically zero drift: Lamperti's problem. / Denisov, Denis; Korshunov, Dmitry; Wachtel, Vitali.
Cambridge: Cambridge University Press, 2025. 428 p. (New Mathematical Monographs; Vol. 51).

Research output: Book/Report/Proceedings › Book

Harvard

Denisov, D, Korshunov, D & Wachtel, V 2025, Markov chains with asymptotically zero drift: Lamperti's problem. New Mathematical Monographs, vol. 51, Cambridge University Press, Cambridge. https://doi.org/10.1017/9781009554237

APA

Denisov, D., Korshunov, D., & Wachtel, V. (2025). Markov chains with asymptotically zero drift: Lamperti's problem. (New Mathematical Monographs; Vol. 51). Cambridge University Press. https://doi.org/10.1017/9781009554237

Vancouver

Denisov D, Korshunov D, Wachtel V. Markov chains with asymptotically zero drift: Lamperti's problem. Cambridge: Cambridge University Press, 2025. 428 p. (New Mathematical Monographs). doi: 10.1017/9781009554237

Author

Denisov, Denis ; Korshunov, Dmitry ; Wachtel, Vitali. / Markov chains with asymptotically zero drift : Lamperti's problem. Cambridge : Cambridge University Press, 2025. 428 p. (New Mathematical Monographs).

Bibtex

@book{b3f97072d04149af9bcf5e80de5ea552,
title = "Markov chains with asymptotically zero drift: Lamperti's problem",
abstract = "This text examines Markov chains whose drift tends to zero at infinity, a topicsometimes referred to as Lamperti{\textquoteright}s problem. It can be considered a subcategory of random walks, which are helpful in studying stochastic models such as branching processes and queueing systems.Drawing on Doob{\textquoteright}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 chain 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.",
author = "Denis Denisov and Dmitry Korshunov and Vitali Wachtel",
year = "2025",
month = may,
day = "8",
doi = "10.1017/9781009554237",
language = "English",
isbn = "9781009554220",
series = "New Mathematical Monographs",
publisher = "Cambridge University Press",
address = "United Kingdom",

}

RIS

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T1 - Markov chains with asymptotically zero drift

T2 - Lamperti's problem

AU - Denisov, Denis

AU - Korshunov, Dmitry

AU - Wachtel, Vitali

PY - 2025/5/8

Y1 - 2025/5/8

N2 - This text examines Markov chains whose drift tends to zero at infinity, a topicsometimes referred to as Lamperti’s problem. It can be considered a subcategory of random walks, which are helpful in studying stochastic models such as 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 chain 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.

AB - This text examines Markov chains whose drift tends to zero at infinity, a topicsometimes referred to as Lamperti’s problem. It can be considered a subcategory of random walks, which are helpful in studying stochastic models such as 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 chain 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.

U2 - 10.1017/9781009554237

DO - 10.1017/9781009554237

M3 - Book

SN - 9781009554220

T3 - New Mathematical Monographs

BT - Markov chains with asymptotically zero drift

PB - Cambridge University Press

CY - Cambridge

ER -