CONDITIONAL DISTRIBUTIONS AND WAITING TIMES IN MULTITYPE BRANCHING PROCESSES

被引：0

作者：

Alexander, H. K. ^{[1
,2
]}

机构：

[1] Queens Univ, Kingston, ON K7L 3N6, Canada

[2] ETH, Inst Integrat Biol, CH-8092 Zurich, Switzerland

来源：

ADVANCES IN APPLIED PROBABILITY | 2013年 / 45卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Multitype branching process; probability generating function; waiting time; escape mutant; evolutionary biology; epidemiology; BURST-DEATH MODEL; FIXATION PROBABILITIES; EMERGENCE; ESCAPE; RISK;

D O I：

10.1017/S0001867800006546

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：

In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes overtime, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

引用

页码：692 / 718

页数：27

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