Summary
We give an example that shows that for strongly mixing sequences of random variables with values in infinite-dimensional spaces no analogue to an approximation theorem of Berkes and Philipp holds.
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References
Berkes, István, Philipp, Walter: Almost sure invariance principles for independent and weakly dependent random vectors. Ann. Probability 7, 29–54 (1979)
Dehling, Herold, Philipp, Walter: Almost sure invariance principles for weakly dependent vector-valued random variables, Ann. Probability 10, (1982); to appear
Ibragimov, I.A., Rozanov, Yu.A.: Gaussian random processes. Berlin-Heidelberg-New York: Springer Verlag 1978
Volkonskii, V.A., Rozanov, Yu.A.: Some limit theorems for random functions I. Theory Probability Appl. 4, 178–197 (1959)
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Dehling, H. A note on a theorem of Berkes and Philipp. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 39–42 (1983). https://doi.org/10.1007/BF00532161
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DOI: https://doi.org/10.1007/BF00532161