Sufficient conditions for the filtration of a stationary processes to be standard

Ceillier Gaël, Leuridan Christophe

Let $X$ be a stationary process with values in some $\sigma$-finite measured state space $(E,\mathcal{E},\pi )$, indexed by $\mathbb{Z}$. Call ${\mathcal{F}}^X$ its natural filtration. In…