On Mittag-Leffler distributions and related stochastic processes
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- 作者：Thierry E. Huillet Thierry.Huillet@u-cergy.fr" class="auth_mail" title="E-mail the corresponding author
- 关键词：Mittag-Leffler random variables and processes ; Stochastic growth models ; Neveu branching process with infinite mean ; Immigration and self-decomposability ; Renewal process ; Bolthausen&ndash ; Sznitman coalescent
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2016
- 出版时间：April 2016
- 年：2016
- 卷：296
- 期：Complete
- 页码：181-211
- 全文大小：586 K
文摘
Random variables with Mittag-Leffler distribution can take values either in the set of non-negative integers or in the positive real line. They can be of two different types, one (type-1) heavy-tailed with index source">α∈(0,1), the other (type-2) possessing all its moments. We investigate various stochastic processes where they play a key role, among which: the discrete space/time Neveu branching process, the discrete-space continuous-time Neveu branching process, the continuous space/time Neveu branching process (CSBP) and renewal processes with rare events. Its relation to (discrete or continuous) self-decomposability and branching processes with immigration is emphasized. Special attention will be paid to the Neveu CSBP for its connection with the Bolthausen–Sznitman coalescent. In this context, and following a recent work of Möhle (2015), a type-2 Mittag-Leffler process turns out to be the Siegmund dual to Neveu’s CSBP block-counting process arising in sampling from source">PD(e−t,0). Further combinatorial developments of this model are investigated.