FLEMING-VIOT PROCESSES IN POPULATION-GENETICS

被引：136

作者：

ETHIER, SN ^{[1
]}

KURTZ, TG ^{[1
]}

机构：

[1] UNIV WISCONSIN, DEPT MATH, MADISON, WI 53706 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1993年 / 31卷 / 02期

关键词：

MEASURE-VALUED MARKOV CHAIN; MEASURE-VALUED DIFFUSION PROCESS; MARTINGALE PROBLEM; CONVERGENCE IN DISTRIBUTION; ERGODICITY; INFINITE PARTICLE SYSTEM; REVERSIBILITY; INFINITELY-MANY-NEUTRAL-ALLELES MODEL;

D O I：

10.1137/0331019

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Fleming and Viot [Indiana Univ. Math. J., 28 (1979), pp. 817-843] introduced a class of probability-measure-valued diffusion processes that has attracted the interest of both pure and applied probabilists. This paper surveys the subject of Fleming-Viot processes as it relates to population genetics. Topics include: 1. Introduction. 2. Some measure-valued Markov chains. 2.1. A diploid model. 2.2. The Wright-Fisher model. 2.3. A Moran model. 3. The Fleming-Viot process: characterization. 4. Convergence. 5. Ergodicity. 6. An infinite particle system. 7. Bounded mutation operators. 8. Reversibility. 9. Examples. 9.1. Continuous-state stepwise-mutation model. 9.2. Infinitely-many-neutral-alleles model. 9.3. Infinitely-many-neutral-alleles model with ages. 9.4. Two-locus model with recombination. 9.5. n-locus model with gene conversion. 9.6. Infinitely-many-sites model without recombination. 9.7. Infinitely-many-neutral-alleles model with allelic genealogies.

引用

页码：345 / 386

页数：42

共 81 条

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