[1]杨旭,国洪松*.基于临界Galton -Watson过程的随机游动的大偏差[J].延边大学学报(自然科学版),2020,46(02):101-105155.
　YANG Xu,GUO Hongsong*.Large deviation of random walk indexed bycritical Galton-Watson process[J].Journal of Yanbian University,2020,46(02):101-105155.
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基于临界Galton -Watson过程的随机游动的大偏差

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第46卷 期数: 2020年02期 页码: 101-105155 栏目: 基础科学研究 出版日期: 2020-08-18
Title:
Large deviation of random walk indexed by critical Galton-Watson process
文章编号:
1004-4353(2020)02-0101-06
作者:
杨旭;  国洪松*
( 中国矿业大学(北京)理学院, 北京 100083 )
Author(s):
YANG Xu;  GUO Hongsong*
( College of Science, China University of Mining & Technology(Beijing), Beijing 100083, China )
关键词:
大偏差概率;  临界Galton -Watson过程;  条件概率;  Fuk -Nagaev不等式
Keywords:
large deviation probability;  critical Galton -Watson process;  conditional probability;  Fuk -Nagaev inequality
分类号:
O211.65
文献标志码:
A
摘要:
针对一族独立同分布的随机变量{Xk}的和SZ<sup></sup>n=Z<sup>nk=1Xk(Zn为临界Galton-Watson过程的第n代个体数),利用随机游动和概率论的知识研究了Rn:=SZ<sup></sup>n/Zn的渐近性质以及在{Zn>0}条件下的SZ<sup></sup>n的大偏差.研究结果表明, Rn的规范偏差概率有非退化的极限,并且其大偏差规范化后收敛到正常数.
Abstract:
Consider the sum SZ<sup></sup>n=Z<sup>nk=1Xk of a family of independent and identically distributed random variables {Xk}, where Zn is the number of individuals of a critical Galton -Watson process in the generation n. The asymptotic properties of the ratio Rn:=SZ<sup></sup>n/Zn and the large deviation of SZ<sup></sup>n under {Zn>0} are studied by using the properties of random walks and branching processes. The proofs are given in detail that the normal deviation probability of Rn has nondegenerate limit and the large deviation probabilities of Rn after normalization converge to a positive constant.

参考文献/References:

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备注/Memo

收稿日期: 2020-06-01 基金项目: 国家自然科学基金资助项目(11801556)
*通信作者: 国洪松(1989—),女,博士,讲师,研究方向为分支过程和随机树.

更新日期/Last Update: 2020-08-18