Summary
A direct proof is given of the Tanny (1974) result that for certain non-decreasing sequences a n , it is true that lim supa n −1 X n = 0 or + ∞ with probability one for all ergodic stationary sequences X n . The condition on a n is shown to be necessary. For all non-decreasing a n and stationary X n , lim sup a n −1 X n= lim sup a n −1 X −n a.s. Similar continuous-time theorems are also given.
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This research supported in part by the Natural Sciences and Engineering Research Council of Canada
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O'Brien, G.L. The occurrence of large values in stationary sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 347–353 (1982). https://doi.org/10.1007/BF00539834
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DOI: https://doi.org/10.1007/BF00539834