Geodesic
Ergodic Type Theorems for Gaussian Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 40-45

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It is assumed that the correlation matrix $(\rho _{ij})$ of a Gaussian system $(X_i,\,i=1,2,\dots)$ generates a bounded linear operator on $l^1$. Under this assumption, ergodic type theorems are discussed. 
@article{TM_2005_248_a3,
     author = {M. Be\'ska and Z. Ciesielski},
     title = {Ergodic {Type} {Theorems} for {Gaussian} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {40--45},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_248_a3/}
}
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M. Beśka; Z. Ciesielski. Ergodic Type Theorems for Gaussian Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 40-45. http://geodesic.mathdoc.fr/item/TM_2005_248_a3/