SEMI-MIN-STABLE PROCESSES

• 成果类型: Article
• 署名作者: PENROSE, MD
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989700
• 发表日期: 1992
• 页码: 1450-1463
• 关键词: sample

摘要

We define a semi-min-stable (SMS) process Y(t) in [0, infinity) to be one which is stable under the simultaneous operations of taking the minima of n independent copies of Y(t) (pointwise over time t) and rescaling space and time. We show that the only possible rescaling of time is by a fixed power of n and that SMS processes are essentially the only possible weak limits for large m of a process obtained by taking the minimum, pointwise over t, of m independent copies of a given process and then rescaling space and time. We describe the representation of a SMS process as the minimum of a Poisson process on a function space. We obtain a partial characterization of sample continuous SMS processes, similar to that of de Haan in the case of max-stable processes.