Geodesic
Ratio Limit Theorems
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 403-407

Voir la notice de l'article provenant de la source Cambridge University Press

Let be an adapted sequence of integrable random variables on the probability space . Let us set .The following result can be immediately derived from Brown [2]: 
Mucci, A. G. Ratio Limit Theorems. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 403-407. doi: 10.4153/CJM-1976-040-8
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[1] 1. Breiman, L., Optimal gambling systems for favorable games, Fourth Berkeley Symposium on Probability and Mathematical Statistics, Vol. 1 (1961), 65–78. Google Scholar

[2] 2. Brown, B. M., A conditional setting for some theorems associated with the strong law, Z. Wahrscheinlichkeitstheorie 19 (1971), 274–280. Google Scholar

[3] 3. Dubins, L. E. and Freedman, D. A., A sharper form of the Borel-Cantelli lemma and the strong law, Annals of Mathematical Statistics 36 (1965), 800–807. Google Scholar

[4] 4. Freedman, D. A., Another note of the Borel-Cantelli lemma and the strong law with the Poisson approximation as a by-product, Annals of Probability 1 (1973), 910–925. Google Scholar

[5] 5. Stout, W. F., Almost sure convergence (Academic Press, 1974). Google Scholar

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