Laplacian Generated by the Gaussian Measure and Ergodic Theorem - Bogdanskii, Yu. V.; Sanzharevskii, Ya. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
We consider the Laplacian generated by the Gaussian measure on a separable Hilbert space and prove the ergodic theorem for the corresponding one-parameter semigroup.