Convolution equivalence and distributions of random sums

• 成果类型: Article
• 署名作者: Watanabe, Toshiro
• 署名单位: University of Aizu
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0109-7
• 发表日期: 2008
• 页码: 367-397
• 关键词: infinite-divisibility; subexponential distributions; Levy processes; random-walks; tails; asymptotics; probability; overshoots; closure; LIMITS

摘要

A serious gap in the Proof of Pakes's paper on the convolution equivalence of infinitely divisible distributions on the line is completely closed. It completes the real analytic approach to Sgibnev's theorem. Then the convolution equivalence of random sums of IID random variables is discussed. Some of the results are applied to random walks and Levy processes. In particular, results of Bertoin and Doney and of Korshunov on the distribution tail of the supremum of a random walk are improved. Finally, an extension of Rogozin's theorem is proved.