Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-28T20:26:54.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic absorption probabilities for a Poisson process

Published online by Cambridge University Press:  14 July 2016

S. Gallot
S. Gallot*
Affiliation:
University of Manchester
Get access Rights & Permissions [Opens in a new window]

Extract

An expression is found (Theorem 1) for the probability that a sample function of a Poisson process never exceeds some given function and some examples are given.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 445 - 452
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Baxter, G. and Donsker, M. D. (1957) On the distribution of the supremum functional for processes with stationary independent increments. Trans. Amer. Math. Soc. 85, 73–87.Google Scholar
[2] Boas, R. P. (1954) Entire Functions. Academic Press Inc. Google Scholar
[3] Daniels, H. E. (1963) The Poisson process with a curved absorbing boundary. Bulletin of the I.S.I., 34th Session, Ottawa. 994–1008.Google Scholar
[4] Loève, M. (1963) Probability Theory, 3rd edition. Van Nostrand Co. Inc. Google Scholar
[5] Pyke, R. (1959) The supremum and infimum of the Poisson process. Ann. Math. Statist. 30, 568–576.CrossRefGoogle Scholar
[6] Whittle, P. (1961) Some exact results for one-sided distribution tests of the Kolmogorov-Smirnov type. Ann. Math. Statist. 32, 499–505.Google Scholar