Screen LibraryNon-homogeneous random walks : Lyapunov function methods for near-critical stochastic systems /
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| Main Authors: | |
|---|---|
| Group Author: | ; |
| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge : |
| Publication Dates: | 2017. |
| Literature type: | Book |
| Language: | English |
| Series: |
Cambridge tracts in mathematics ;
209 |
| Subjects: | |
| Carrier Form: | xviii, 363 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages 344-360) and index. |
| ISBN: |
9781107026698 1107026695 |
| Index Number: | QA274 |
| CLC: | O211.6 |
| Call Number: | O211.6/M548 |
| Contents: |
Machine generated contents note: Introduction -- Random Walks -- Simple Random Walk -- Lamperti's Problem -- General Random Walk -- Recurrence and Transience -- Angular Asymptotics -- Centrally Biased Random Walks -- Bibliographical Notes -- Semimartingale Approach and Markov Chains -- Definitions -- An Introductory Example -- Fundamental Semimartingale Facts -- Displacement and Exit Estimates -- Recurrence and Transience Criteria for Markov Chains -- Expectations of Hitting Times and Positive Recurrence -- Moments of Hitting Times -- Growth Bounds on Trajectories -- Bibliograpical Notes -- Markovian Case -- General Case -- Lyapunov Functions -- Recurrence Classification -- Irreducibility and Regeneration -- Moments and Tails of Passage Times -- Excursion Durations and Maxima -- Almost-Sure Bounds on Trajectories -- Transient Theory in the Critical Case -- Nullity and Weak Limits -- Supercritical Case -- Proofs for the Markovian Case -- Many-Dimensional Random Walks -- Elliptic Random Walks -- Controlled Driftless Random Walks -- Range and Local Time of Many-Dimensional Martingales -- Heavy Tails -- Chapter Overview -- Directional Transience -- Oscillating Random Walk -- Further Applications -- Random Walk in Random Environment -- Random Strings in Random Environment -- Stochastic Billiards -- Exclusion and Voter Models -- Markov Chains in Continuous Time -- Introduction and Notation -- Existence and Non-existence of Moments of Passage Times -- Explosion and Implosion -- Applications -- Bibliographical Notes. |