The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes

• 成果类型: Article
• 署名作者: Mikosch, Thomas; Moser, Martin
• 署名单位: University of Copenhagen; Technical University of Munich; Technical University of Munich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0427-2
• 发表日期: 2013
• 页码: 249-272
• 关键词: sample autocorrelations; extremal behavior; random-variables; Moving averages; EQUATIONS; THEOREMS

摘要

We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fr,chet distributed random variable.