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Asymptotic absorption probabilities for a Poisson process

Published online by Cambridge University Press:  14 July 2016

S. Gallot
S. Gallot*
Affiliation:
University of Manchester
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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 

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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