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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 2,
pages 373 - 381
 

ON SOME CONNECTIONS BETWEEN RANDOM PARTITIONS OF THE UNIT SEGMENT AND THE POISSON PROCESS

Krzysztof Kaniowski

Abstract: Let D t be the diameter of a partition of the interval [0,t] by renewal moments of a standard Poisson process. Then D /lnt-- > 1 t for t-- > oo , in probability. Other theorems on diameters are obtained. Jajte’s theorem on random partitions of the unit segment is used.

1991 AMS Mathematics Subject Classification: 60F10, 60G5S.

Key words and phrases: -

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