SAMPLE AND ERGODIC PROPERTIES OF SOME MIN-STABLE PROCESSES

• 成果类型: Article
• 署名作者: WEINTRAUB, KS
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990447
• 发表日期: 1991
• 页码: 706-723
• 关键词: multivariate

摘要

A random vector is min-stable (or jointly negative exponential) if any weighted minimum of its components has a negative exponential distribution. The vectors can be subordinated to a two-dimensional homogeneous Poisson point process through positive L1 functions called spectral functions. A critical feature of this representation is the point of the Poisson process, called the location, that defines a min-stable random variable. A measure of association between min-stable random variables is used to define mixing conditions for min-stable processes. The association between two min-stable random variables X1 and X2 is defined as the probability that they share the same location and is denoted by q(X1, X2). Mixing criteria for a min-stable process X(t) are defined by how fast the association between X(t) and X(t + s) goes to zero as s --> infinity. For some stationary processes (including the moving-minimum process), conditions on the spectral functions are derived in order that the processes satisfy mixing conditions.