Splitting intervals. (English) Zbl 0601.60028

Brennan, Michael D.; Durrett, Richard

Ann. Probab. 14, 1024-1036 (1986).

For a class of discrete and continuous time stochastic processes in which the unit interval undergoes random subdivision at successive points \(X_ i\), \(i\geq 1\), in such a way that an interval of length L splits with probability (or exponential rate) proportional to \(L^{\alpha}\), \(\alpha \in [-\infty,+\infty]\), into two random intervals, the limit behavior in the weak convergence sense of the empirical distribution function is discussed in the cases \(\alpha\in [-\infty,0)\) and \(\alpha\in (0,1)\).

Reviewer: N.Kalinauskaitė

MSC:

60F15	Strong limit theorems
60K99	Special processes
60F05	Central limit and other weak theorems

Keywords:

splitting intervals; limit behavior in the weak convergence; empirical distribution function