Skip Navigation

Journal of the London Mathematical Society 1988 s2-38(1):179-192; doi:10.1112/jlms/s2-38.1.179
© 1988 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Grübel, R.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

Harmonic Renewal Sequences and the First Positive Sum

Rudolf Grübel

Department of Mathematics, Imperial College of Science and Technology London SW7 2BZ

With a probability distribution p on the integers, regarded as a sequence, we associate its harmonic renewal sequence Formula. Let h+ = v({delta}1), h = v(1/2({delta}-1 + {delta}1)), where {delta}x is the unit mass at x. We characterize summability of v(p)–h+, v(p)–h in terms of p. This enables us to compare the asymptotic behaviour of p and v(p) and to obtain expansions.

Harmonic renewal sequences are important for lattice-type random walks. Our results lead to tail expansions for ladder height distributions.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.