带迁移的平稳二阶Galton-Watson过程的尾部行为

IF 0.7 Q3 STATISTICS & PROBABILITY

Modern Stochastics-Theory and Applications Pub Date : 2018-01-24 DOI:10.15559/20-VMSTA161

M. Barczy, Z. Bősze, G. Pap

{"title":"带迁移的平稳二阶Galton-Watson过程的尾部行为","authors":"M. Barczy, Z. Bősze, G. Pap","doi":"10.15559/20-VMSTA161","DOIUrl":null,"url":null,"abstract":"A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"414 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2018-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On tail behaviour of stationary second-order Galton–Watson processes with immigration\",\"authors\":\"M. Barczy, Z. Bősze, G. Pap\",\"doi\":\"10.15559/20-VMSTA161\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.\",\"PeriodicalId\":42685,\"journal\":{\"name\":\"Modern Stochastics-Theory and Applications\",\"volume\":\"414 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2018-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modern Stochastics-Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15559/20-VMSTA161\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modern Stochastics-Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15559/20-VMSTA161","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 4

摘要

带迁移的二阶高尔顿-沃森过程可以表示为带迁移的2型高尔顿-沃森过程的坐标过程。给出了二阶带迁移的Galton-Watson过程的子代分布和迁移分布的充分条件，在此条件下，相应的2型带迁移的Galton-Watson过程具有唯一的平稳分布，其共同边际是规则变化的。在证明过程中，给出了在种群初始大小独立且有规律变化的条件下，二阶高尔顿-沃森过程(无迁移)在任何固定时间的分布是有规律变化的充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On tail behaviour of stationary second-order Galton–Watson processes with immigration

A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Modern Stochastics-Theory and Applications STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

50.00%

发文量

审稿时长

10 weeks