Darling-Erdos theorems for normalized sums of IID variables close to a stable law

• 成果类型: Article
• 署名作者: Bertoin, J
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022855652
• 发表日期: 1998
• 页码: 832-852
• 关键词: stationary

摘要

Let xi, xi(1), be i.i.d. real-valued random variables and S-n = xi(1) + ... + xi(n). In the case when the distribution of xi is close to a stable (alpha) law for some alpha is an element of (0, 1) boolean OR (1, 2), we investigate the asymptotic behavior in distribution of the maximum of normalized sums, max(k = 1, ..., n) k(-1/alpha) S-k. This completes the Darling-Erdos limit theorem for the case alpha = 2.