Non-Homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems

ISBN-13: 9781107026698 / Angielski / Twarda / 2016 / 382 str.

Mikhail Menshikov; Serguei Popov; Andrew Wade

Opis

A modern presentation of the 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks.

Recenzje

'This book gives a comprehensive account of the study of random walks with spatially non-homogeneous transition kernels. The main theme is to study recurrence versus transience and moments of passage times, as well as path asymptotics, by constructing suitable Lyapunov functions, which define semi-martingales when composed with the random walk. Of special interest are the Lamperti processes, which are stochastic processes on [0, ∞) with drift vanishing asymptotically on the order of 1/x as the space variable x tends to infinity. … Each chapter ends with detailed bibliographical notes.' Rongfeng Sun, Mathematical Reviews

Spis treści

1. Introduction; 2. Semimartingale approach and Markov chains; 3. Lamperti's problem; 4. Many-dimensional random walks; 5. Heavy tails; 6. Further applications; 7. Markov chains in continuous time; Glossary of named assumptions; Bibliography; Index.