论文标题
适合组的对称稳定过程
Symmetric Stable Processes on Amenable Groups
论文作者
论文摘要
我们表明，如果$ g $是一个可计数的群体，那么每个固定的非高斯对称$α$ stable（s $α$ s）的过程由$ g $索引时，只有当它弱混合时，并且仅当它是ergodic的，并且仅当它的Rosinski Minimal Spectral Sepanditation null null。这扩展了$ \ mathbb {z}^d $的结果，并在所有可计数的amenable组中回答了P. Roy在离散的nilpotent组上的问题。结果，我们在Heisenberg组和许多Abelian群体上构建了（0,2）的所有$α$（0,2），固定的S $α$ S $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ s $ cAUM的混合量较弱，但并非强烈混合。
We show that if $G$ is a countable amenable group, then every stationary non-Gaussian symmetric $α$-stable (S$α$S) process indexed by $G$ is ergodic if and only if it is weakly-mixing, and it is ergodic if and only if its Rosinski minimal spectral representation is null. This extends the results for $\mathbb{Z}^d$, and answers a question of P. Roy on discrete nilpotent groups to the extent of all countable amenable groups. As a result we construct on the Heisenberg group and on many Abelian groups, for all $α$ in (0,2), stationary S$α$S processes that are weakly-mixing but not strongly-mixing.
