ERGODIC PROPERTIES OF SUM- AND MAX-STABLE STATIONARY RANDOM FIELDS VIA NULL AND POSITIVE GROUP ACTIONS

• 成果类型: Article
• 署名作者: Wang, Yizao; Roy, Parthanil; Stoev, Stilian A.
• 署名单位: University of Michigan System; University of Michigan; Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP732
• 发表日期: 2013
• 页码: 206-228
• 关键词: representations

摘要

We establish characterization results for the ergodicity of stationary symmetric alpha-stable (S alpha S) and alpha-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in the multiparameter setting, that is, a stationary S alpha S (0 < alpha < 2) random field is ergodic (or, equivalently, weakly mixing) if and only if it is generated by a null group action. Similar results are also established for max-stable random fields. The key ingredient is the adaption of a characterization of positive/null recurrence of group actions by Takahashi [Kadai Math. Sem. Rep. 23 (1971) 131-143], which is dimension-free and different from the one used by Samorodnitsky.