Hostname: page-component-7b9c58cd5d-6tpvb Total loading time: 0 Render date: 2025-03-15T05:17:42.101Z Has data issue: false hasContentIssue false
  • English
  • Français

The limit theorem for aperiodic discrete renewal processes

Published online by Cambridge University Press:  09 April 2009

P. D. Finch
P. D. Finch
Affiliation:
The Australian National University, Canberra.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A discrete renewal process is a sequence {X4} of independently and inentically distributed random variables which can take on only those values which are positive integral multiples of a positive real number δ. For notational convenience we take δ = 1 and write where .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1964 , pp. 122 - 128
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Doob, J. L., Renewal theory from the point of view of the theory of probability, Trans. Amer. Math. Soc. 63, 422–38 (1948).CrossRefGoogle Scholar
[2]Doob, J. L., Stochastic Processes, New York, Wiley (1953).Google Scholar
[3]Erdös, P., Feller, W., and Pollard, H., A theorem on power series, Bull. Amer. Math. Soc. 55, 201–204 (1949).CrossRefGoogle Scholar
[4]Feller, W., A simple proof for renewal theorems, Comm. Pure Appl. Math. 14, 285–293 (1961).CrossRefGoogle Scholar
[5]Kolmogorov, A., Anfangagründe der Theorie der Markoffschen Ketten mit unendlich vielen möglichen Zuständen, Mat. Sbornik. N.S. 1, 607–610 (1936).Google Scholar