ON SOME CONNECTIONS BETWEEN RANDOM PARTITIONS OF THE
UNIT SEGMENT AND THE POISSON PROCESS
Abstract: Let be the diameter of a partition of the interval by renewal moments of
a standard Poisson process. Then for 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.
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