Jump to ContentJump to Main Navigation
First Steps in Random WalksFrom Tools to Applications$
Users without a subscription are not able to see the full content.

J. Klafter and I. M. Sokolov

Print publication date: 2011

Print ISBN-13: 9780199234868

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199234868.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 January 2021

Generating functions and applications

Generating functions and applications

(p.17) 2 Generating functions and applications
First Steps in Random Walks

J. Klafter

I.M. Sokolov

Oxford University Press

This chapter concentrates on the properties of the walks which do not immediately follow from the distribution of the particle's position after n steps, like the first passage and return probabilities. These are most elegantly obtained via generating functions of the corresponding distributions. Again, the necessary mathematical toolbox is first introduced and discussed, including definition and main properties of generating functions and Tauberian theorems giving a nice method of approximate restoration of probability distributions from their generating functions. Then it concentrates on explicit calculations of first passage and return probabilities of the lattice walks, as well on the mean number of distinct sites visited by a walk of n steps. Some properties of off‐lattice walks are discussed as well.

Keywords:   generating functions, Tauberian theorems, first passage and return probabilities, distinct visited sites, Sparre Andersen theorem

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .