期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
页码：53-66
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider the area A =R 10 (P1i=1 Xi(t)) dt of a self-similar fragmentationprocess X = (X(t), t 0) with negative index. We characterize the law of Aby an integro-differential equation. The latter may be viewed as the infinitesimalversion of a recursive distribution equation that arises naturally in this setting. Inthe case of binary splitting, this yields a recursive formula for the entire momentsof A which generalizes known results for the area of the Brownian excursion.
