| Título: | Random Discrete Distributions Derived from Self-Similar Random Sets |
| Autores: |
Pitman, Jim; University of California, Berkeley Yor, Marc; Université Pierre et Marie Curie |
| Fecha: | 1996-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics interval partition, zero set, excursion lengths, regenerative set, structural distribution. 60G18, 60G57, 60K05. |
| Descripción: | A model is proposed for a decreasing sequence of random variables $(V_1, V_2, \cdots)$ with $\sum_n V_n = 1$, which generalizes the Poisson-Dirichlet distribution and the distribution of ranked lengths of excursions of a Brownian motion or recurrent Bessel process. Let $V_n$ be the length of the $n$th longest component interval of $[0,1]\backslash Z$, where $Z$ is an a.s. non-empty random closed of $(0,\infty)$ of Lebesgue measure $0$, and $Z$ is self-similar, i.e. $cZ$ has the same distribution as $Z$ for every $c > 0$. Then for $0 \le a < b \le 1$ the expected number of $n$'s such that $V_n \in (a,b)$ equals $\int_a^b v^{-1} F(dv)$ where the structural distribution $F$ is identical to the distribution of $1 - \sup ( Z \cap [0,1] )$. Then $F(dv) = f(v)dv$ where $(1-v) f(v)$ is a decreasing function of $v$, and every such probability distribution $F$ on $[0,1]$ can arise from this construction. |
| Idioma: | Inglés |
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