[For the entire collection see Zbl 0718.00011.]
The authors define the dynamical functional \(\Phi\) of a stationary stochastically continuous process \(X=\{X_ t:\) \(t\in {\mathbb{R}}\}\) by the formula \(\Phi (Y,t)=E \exp (i(Y\circ \theta_ t-Y)),\) where Y is any element of the closure of \(lin(X_ t:\) \(t\in {\mathbb{R}})\) with respect to the topology of convergence in measure, and \(\theta_ t\) is the shift transformation. They prove that X is ergodic if and only if \[ \lim_{T\to \infty}T^{-1}\int^{T}_{0}\Phi (Y,t)dt=| E \exp (iY)|^ 2 \] for any Y. An application is given to symmetric stable processes by unifying two equivalent conditions for ergodicity given previously.