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Potential Functions of Random Walks in ℤ with Infinite Variance Estimates and Applications /

This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, y...

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Bibliographic Details
Main Author: Uchiyama, Kôhei (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Cham : Springer Nature Switzerland : Imprint: Springer, 2023.
Edition:1st ed. 2023.
Series:Lecture Notes in Mathematics, 2338
Subjects:
Probabilities.
Markov processes.
Probability Theory.
Markov Process.
Online Access:https://doi.org/10.1007/978-3-031-41020-8
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Table of Contents:
  • Preface
  • Introduction
  • Preliminaries
  • Bounds of the Potential Function
  • Some Explicit Asymptotic Forms of a(x)
  • Applications Under m+/m → 0
  • The Two-Sided Exit Problem – General Case
  • The Two-Sided Exit Problem for Relatively Stable Walks
  • Absorption Problems for Asymptotically Stable Random Walks
  • Asymptotically Stable RandomWalks Killed Upon Hitting a Finite Set
  • Appendix
  • References
  • Notation Index
  • Subject Index.

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