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PDF(476 KB)
PDF(476 KB)
稳定积分的弱收敛
Weak Convergence of Stable Integrals
令{X；Xn ≥ 1}是一列严平稳的随机变量，且其分布F在一个α-稳定分布的吸引场，这里0 < α < 1.本文考虑∑i=1nfn（β，i/n）（Xi）/（an）的弱收敛性.不同于经典意义下的随机过程弱收敛，本文将∑i=1nfn（β，i/n）（Xi）/（an）看作β变化的随机元，利用点过程收敛方法得到了其弱收敛性.
Let {X; Xn ≥ 1} be a strictly random variable series, and its distribution F in a α-stable distribution attracting field, where 0 < α < 1. In this paper, we consider the weak convergence of ∑i=1nfn(β, i/n)(Xi)/(an). Different from the classical weak convergence, ∑i=1nfn(β, i/n)(Xi)/(an) are regarded as a random elements with respect to β's change, and its weak convergence is obtained by using the point process convergence method.
M1-拓扑 / 弱收敛 / 点过程 / &alpha / -稳定分布 {{custom_keyword}} /
M1-topology / weak convergence / point process / α-stable distribution {{custom_keyword}} /
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国家自然科学基金（11701331）；山东省自然科学基金（ZR2017QA007）；山东大学基本科研业务费（2016GN019）；浙江省自然科学基金（LQ18A010006）；浙江省一流学科A类（浙江财经大学统计学）资助（Z0111116008/013）；浙江省教育厅科研项目资助（Y201635727）
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