Length laws for random subdivision of longest intervals

Michael D. Brennan

Stochastic Processes and their Applications, 1986, vol. 22, issue 1, 17-26

Abstract: [0, 1] is partitioned by randomly splitting the longest subinterval, of length L, into two intervals of lengths LV and L(1 - V). V is independent of the past with a fixed distribution on (0, 1) If there are n subintervals and Ln is the length of a randomly chosen subinterval, then P(nLn [set membership, variant] dy) [congruent with] y-1P(K exp(-T0) [set membership, variant] dy) where K = E(exp(T0)) and T0 is the first renewal in a stationary renewa process constructed from V.

Keywords: random; subdivision; splitting; process; emperical; distribution; function; limit; lae; limit; law; stationary; renewal; process (search for similar items in EconPapers)
Date: 1986
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