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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 9, pp. 1172–1180, September, 2015.
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Bogdanskii, Y.V., Sanzharevskii, Y.Y. Laplacian Generated by the Gaussian Measure and Ergodic Theorem. Ukr Math J 67, 1316–1326 (2016). https://doi.org/10.1007/s11253-016-1155-z
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DOI: https://doi.org/10.1007/s11253-016-1155-z