On some connections between random partitions of the unit segment and the Poisson process

• Autorzy: Kaniowski K.
• Języki publikacji: EN

Abstrakty

EN

Let D_t be the diameter of a partition of the interval [0, t] by renewal moments of a standard Poisson process. Then D_t/ln_t → 1 for t →∞, in probability. Other theorems on diameters are obtained. Jajte’s theorem on random partitions of the unit segment is used.

Słowa kluczowe

EN

Poisson process; diameter; Jajte’s theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 373--381
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Kaniowski K.

• Faculty of Mathematics, University of Łódź, 90-238 Łódź, Banacha 22, Poland

Bibliografia

• [1] D. A. Darling, On a class of problems related to the random division of an interval, Ann. Math. Statist. 24 (1953), pp. 239-253.
• [2] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, New York 1966.
• [3] R. Jajte, On random partitions of the segment, Bull. Acad. Polon. Sci. 19 (1971), pp. 231-233.