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On some Asymptotic Properties of Poisson Process

Published online by Cambridge University Press:  22 January 2016

Takeyuki Hida
Takeyuki Hida*
Affiliation:
Mathematical Institute, Aichi Gakugei University
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The Poisson process , as is well-known, is a temporally and spatially homogeneous Markoff process satisfying

(1)

(2)

where k is a non-negative integer and λ is a positive constant. In this note we consider the random variable Lm(ω) which denotes the length of t-interval such that X(t, w) = m (m = 0, 1, 2,…) and some of other properties concerning them.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 29 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Nishida, T., On the inverse function of Poisson process. Mathematica Japonicae. Vol. II No. 3. (1952) pp. 135–142.Google Scholar
[2] Lévy, P., Processus stochastiques et mouvement brownien. (1948) p. 182.Google Scholar
[3] Darling, D. A., The influence of the maximum term in the addition of independent random variables. Transactions of the American Mathematical Society. Vol. 73. No. 1 (1952) pp. 95–107.CrossRefGoogle Scholar
[4] Ōta, T., On some properties of Poisson process I. Bulletin of the Aichi Gakugei University. Vol. 2. (1953). pp. 1–6.Google Scholar