LIMIT THEOREMS FOR SMOLUCHOWSKI DYNAMICS ASSOCIATED WITH CRITICAL CONTINUOUS-STATE BRANCHING PROCESSES

被引：8

作者：

Iyer, Gautam ^{[1
]}

Leger, Nicholas ^{[1
]}

Pego, Robert L. ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2015年 / 25卷 / 02期

基金：

美国国家科学基金会;

关键词：

Continuous-state branching process; critical branching; limit theorem; scaling limit; Smoluchowski equation; coagulation; self-similar solution; Mittag-Leffler series; regular variation; Bernstein function; COAGULATION EQUATION; ASYMPTOTIC-BEHAVIOR; CONTINUOUS-TIME;

D O I：

10.1214/14-AAP1008

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuous-state branching theory. In particular, this equation governs the evolution of the Levy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) almost surely. We show that a nondegenerate scaling limit of the Levy measure (and the process) exists if and only if the branching mechanism is regularly varying at 0. When the branching mechanism is regularly varying, we characterize nondegenerate scaling limits of arbitrary finite-measure solutions in terms of generalized Mittag-Leffier series.

引用

页码：675 / 713

页数：39

共 23 条

[1]

[Anonymous], 2006, INTRO LECT FLUCTUATI

[2]

[Anonymous], 1989, ENCY MATH ITS APPL

[3]

Bauer H., 2001, DEGRUYTER STUDIES MA, V26

[4]

Bertoin J, 2002, ANN APPL PROBAB, V12, P547