有根树上的分支平稳max-稳定随机场
Branch-stationary max-stable fields on rooted trees
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中文总结 AI 辅助
该研究针对有根树上的max-稳定随机场，刻画其分支平稳性，给出多种构造方式并推导相关copula，证明可数分支树可加性无需满足零-一律。
中文摘要 AI 辅助
本文研究有根树上的max-稳定随机场，针对向后代子树的平移问题展开分析。分支-布朗-雷斯尼克（Branch-Brown--Resnick）平稳性通过齐次谱类、带孔尾测度及局部谱尾场进行刻画；对于对数正态表示，其等价于变异函数在添加公共前缀下的不变性。我们给出高斯、max-自回归、再生级联及自由群簇构造，证明可数分支树上的可加性无需满足零-一律，还推导了相关的分支不变极值与Archimax copula。
英文摘要
In this contribution we study max-stable random fields on the rooted tree under shifts to descendant subtrees. Branch-Brown--Resnick stationarity is characterised through homogeneous spectral classes, punctured tail measures, and local spectral tail fields. For lognormal representers, it is equivalent to invariance of the variogram under addition of a common prefix. We give Gaussian, max-autoregressive, regenerative cascade, and free-group cluster constructions, and show that summability on countably branching trees need not satisfy a zero--one law. We also derive the associated branch-invariant extreme-value and Archimax copulas.
