Sums of stationary sequences cannot grow slower than linearly
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- by Harry Kesten PDF
- Proc. Amer. Math. Soc. 49 (1975), 205-211 Request permission
Abstract:
It is shown that for a stationary sequence of random variables ${X_1},{X_2}, \cdots$ one has \[ \lim \inf {n^{ - 1}}\sum \limits _{i = 1}^n {{X_i} > 0} \] a.e. on the set $\{ \Sigma _1^n{X_i} \to \infty ,n \to \infty \}$.References
- Leo Breiman, Probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0229267
- David Tanny, A zero-one law for stationary sequences, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 30 (1974), 139–148. MR 375448, DOI 10.1007/BF00532266
- J. Wolfowitz, Remarks on the notion of recurrence, Bull. Amer. Math. Soc. 55 (1949), 394–395. MR 29109, DOI 10.1090/S0002-9904-1949-09222-4
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 205-211
- MSC: Primary 60F15; Secondary 28A65
- DOI: https://doi.org/10.1090/S0002-9939-1975-0370713-4
- MathSciNet review: 0370713