References
I. Berkes and G. J. Morrow, Strong invariance principles for mixing random fields,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,57 (1981), 15–37.
I. Berkes and W. Philipp, Approximation theorems for independent and weakly dependent random vectors,Annals of Probability,7 (1979), 29–54.
Yu. A. Davidov, The invariance principle for stationary processes,Theor. Probability Appl.,15 (1970), 487–498.
R. L. Dobrushin and P. Major, Non-central limit theorems for non-linear functionals of Gaussian fields,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,50 (1979), 27–52.
A. Dvoretzky, Asymptotic normality for sums of dependent random variables,Proc. Sixth Berkeley Sympos. Math. Statist. Probab. Vol. II, 513–535, Univ. of California Press (1970).
I. A. Ibraginov, Some limit theorems for stationary processes,Theor. Probability Appl.,7 (1962), 349–382.
A. N. Kolmogorov and Yu. A. Rozanov, On strong mixing conditions for stationary Gaussian random processes,Theor. Probability Appl.,5 (1960), 204–208.
J. Kuelbs and W. Philipp, Almost sure invariance principles for partial sums of mixing B-valued random variables,Annals of Probability,8 (1980), 1003–1036.
M. Loève,Probability Theory, Van Nostrand (Toronto-New York-London, 1955).
F. Móricz, Moment inequalities for the maximum of partial sums of random fields,Acta Math. Acad. Sci. Hungar.,39 (1977), 353–366.
F. Móricz, Exponential estimates for the maximum of partial sums II (Random fields),Acta math. Acad. Sci. Hungar.,35 (1980), 361–377.
G. J. Morrow, Invariance principles for Gaussian sequences,Z. Wahrscheinlichkeitstheorie und verw. Gebiete,52 (1980), 115–126.
W. Philipp and W. F. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables,Memoirs of the Amer. Math. Soc. No. 161 (Providence, R. I., 1975).
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Berkes, I. Gaussian approximation of mixing random fields. Acta Math Hung 43, 153–185 (1984). https://doi.org/10.1007/BF01951335
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DOI: https://doi.org/10.1007/BF01951335