Catalytic Branching Processes via Spine Techniques and Renewal Theory

被引：8

作者：

Doering, Leif ^{[1
]}

Roberts, Matthew I. ^{[2
]}

机构：

[1] Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75005 Paris, France

[2] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany

来源：

SEMINAIRE DE PROBABILITES XLV | 2013年 / 2078卷

关键词：

RANDOM-WALK; ASYMPTOTICS;

D O I：

10.1007/978-3-319-00321-4_12

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number of particles in a variation of constants formulation. The long-time behaviour is then deduced from renewal theorems and induction.

引用

页码：305 / 322

页数：18

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