Large deviations for a randomly indexed branching process with immigration

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-09-03 DOI:10.1016/j.spl.2025.110546

Zhenlong Gao

引用次数: 0

Abstract

Consider a supercritical continuous time branching process called randomly indexed branching processes with immigration. Large deviation results are established for the logarithms of such processes. Our results show that when the offspring distribution belongs to the Schröder case, the immigration distribution affects the rate function of the large deviation, while when the offspring distribution belongs to the Böttcher case, the immigration distribution has no effect on the rate function.

查看原文本刊更多论文

具有迁移的随机索引分支过程的大偏差

考虑一个具有迁移的称为随机索引分支过程的超临界连续时间分支过程。对于这些过程的对数，建立了大偏差的结果。我们的研究结果表明，当子代分布属于Schröder情况时，移民分布影响较大偏差的速率函数，而当子代分布属于Böttcher情况时，移民分布对速率函数没有影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.