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随机环境加权分枝过程的方差和Fuk-Nagaev型不等式
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Abstract:
在对随机环境中加权分枝过程(Yn)的研究基础上，考虑其规范化过程Wn的方差![\"\"](\"Edit_00e54826-fa63-4386-a35f-331512f1add9.png\")
及其收敛性，并予以了详细的证明，其中规范化过程为![\"\"](\"Edit_829a214f-7f88-4200-b199-94c5f9899e17.png\")
，![\"\"](\"Edit_8877e56b-ddc1-4d8b-bd44-62ebb143cdd8.png\")
是规范化序列，是随机环境分枝过程相关结论的拓展；并且建立了一个关于统计量![\"\"](\"Edit_dc3f51ab-5ee6-4d2b-a0de-c809a0840573.png\")
的Fuk-Nagaev型不等式。
On the basis of the research on the weighted branching process (Yn) in random environments, the variance ![\"\"](\"Edit_5ab6ad85-e9eb-41b7-beed-37fa4ecb44d3.png\")
and convergence of its normalization process Wn are considered, and the de-tailed proof is provided. The normalization process is ![\"\"](\"Edit_c43d1a3b-ce25-4554-9e6e-07f765148750.png\")
, and ![\"\"](\"Edit_14cc0125-03be-4af3-8395-5cb3b8e3554c.png\")
is the normalized se-quence, which is an extension of the conclusions related to the branching process in random envi-ronments. Besides, we establish a Fuk-Nagaev type inequality for ![\"\"](\"Edit_35c73ebb-aa42-49cd-a34f-bca3699ab597.png\")
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