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.
[1] Dym H., McKean H.P., Gaussian processes, function theory and the inverse spectral problem, Acad. Press, New York, 1976 | MR | Zbl
[2] Gebelein H., “Das statistische Problem der Korrelation als Variations und Eigenwertproblem und sein Zusammenhang mit der Ausgleichsrechnung”, Ztschr. angew. Math. und Mech., 21 (1941), 364–379 | DOI | MR | Zbl
[3] Nelson E., “The free Markoff field”, J. Funct. Anal., 12 (1973), 211–227 | DOI | MR | Zbl
[4] Stroock D.W., Probability theory, Cambridge Univ. Press, Cambridge, 2003 | Zbl