Скачать или смотреть Kolmogorov Maximal Inequality & Hàjek-Rènyi Inequality

In probability theory, Kolmogorov's maximal inequality gives an upperbound on the probability that the partial sums of a collection of zero-mean, finite-variance, independent random variables exceed some specified threshold.
The Hàjek-Rènyi inequality is a useful generalization that allows the sums to be scaled by a positive factor that depends on the number of terms in the sum.

Notes:
https://drive.google.com/file/d/1Qh6s...

Here is an application of the Hàjek-Rènyi inequality to prove the Kolmogorov strong law of large numbers:
   • 15 Continuous Mapping Theorem - Slutsky - ...  

Hajek Renyi Inequality
Original paper:
https://akjournals.com/downloadpdf/jo...
Hájek, J., Rényi, A. Generalization of an inequality of Kolmogorov. Acta Mathematica Academiae Scientiarum Hungaricae 6, 281–283 (1955).