NONSINGULAR GROUP ACTIONS AND STATIONARY S alpha S RANDOM FIELDS

作者：Roy Parthanil^*

来源：Proceedings of the American Mathematical Society, 2010, 138(6): 2195-2202.

DOI：10.1090/S0002-9939-10-10250-0

• Random field
• stable process
• extreme value theory
• maxima
• ergodic theory
• nonsingular group action
• dissipative
• conservative

This paper deals with measurable stationary symmetric stable random fields indexed by R(d) and their relationship with the ergodic theory of nonsingular R(d)-actions. Based on the phenomenal work of Rosinski (2000), we establish extensions of some structure results of stationary S alpha S processes to SaS fields. Depending on the ergodic theoretical nature of the underlying action, we observe different behaviors of the extremes of the field.

• 出版日期2010-6