超临界多型分支过程的自归一化大偏差
Self-Normalized Large Deviations for Supercritical Multitype Branching Processes
摘要: 设{Z(t);t≥0}是一个超临界马尔可夫分支过程。本文研究了超临界多型分支过程在连续时间情况下的自归一化大偏差，这是我们对先前研究的离散时间下的自归一化大偏差进行扩展的结果，得到了连续时间内自标准化大偏差的极限是存在的，且是有限的和正的。
Abstract: Let {Z(t);t≥0} be a supercritical Markov branching processes. In this paper, we study the self-normalized large deviations of the supercritical multitype branching processes in continuous time, this is an extension of previous study of the large deviation of the self-normalization in discrete time. From the above, we obtain that the limit of self-normalized large deviation in continuous time exists and is finite and positive.
文章引用：肖宁洁, 王娟. 超临界多型分支过程的自归一化大偏差[J]. 理论数学, 2022, 12(11): 1843-1850. https://doi.org/10.12677/PM.2022.1211197

参考文献

[1] Li, J., Cheng, L., Pakes, A.G., Chen, A. and Li, L. (2020) Large Deviation Rates for Markov Branching Processes. Analysis and Applications, 18, 447-468. [Google Scholar] [CrossRef] 
[2] Li, J.P. and Meng, W.W. (2017) Regularity Criterion for 2-Type Markov Branching Processes with Immigration. Statistics & Probability Letters, 121, 109-118. [Google Scholar] [CrossRef] 
[3] Li, J., Cheng, L. and Li, L. (2021) Long Time Behaviour for Markovian Branching-Immigration Systems. Discrete Event Dynamic Systems, 31, 37-57. [Google Scholar] [CrossRef] 
[4] Athreya, K.B. (1994) Large Deviation Rates for Branching Processes—I. Single Type Case. The Annals of Applied Probability, 4, 779-790. [Google Scholar] [CrossRef] 
[5] Chu, W. (2018) Self-Normalized Large Deviation for Supercritical Branching Processes. Journal of Applied Probability, 55, 450-458. [Google Scholar] [CrossRef] 
[6] Athreya, K.B. and Vidyashankar, A.N. (1995) Large Deviation Rates for Branching Processes. II. The Multitype Case. The Annals of Applied Probability, 5, 566-576. [Google Scholar] [CrossRef] 
[7] Jones, O.D. (2004) Large Deviations for Supercritical Multitype Branching Processes. Journal of Applied Probability, 41, 703-720. [Google Scholar] [CrossRef] 
[8] Athreya, K.B. and Ney, P.E. (1972) Branching Processes. Springer, New York.
[9] Shao, Q.M. (1997) Self-Normalized Large Deviations. The Annals of Probability, 25, 285-328. [Google Scholar] [CrossRef] 

为你推荐