On the Association of Sum- and Max- Stable Processes

2009/10/12 by Yizao Wang, Wang, Yizao, Stilian Stoev +2
Economics, Econometrics and Finance · Engineering · Mathematics · #60G52 #60G70 #FOS: Mathematics #Fuzzy Systems and Optimization #Probability (math.PR) #Stability and Control of Uncertain Systems #Stochastic processes and financial applications #math.PR #msc:60G52 #msc:60G70

paper · pdf · doi:10.48550/arxiv.0910.2069

arxiv created 2009/10/12 · openalex publication_date 2009/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the notion of association of sum- and max- stable processes from the perspective of linear and max-linear isometries. We establish the appealing results that these two classes of isometries can be identified on a proper space (the extended positive ratio space). This yields a natural way to associate to any max-stable process a sum-stable process. By using this association, we establish connections between structural and classification results for sum- and max- stable processes.

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