On the strong law of large numbers for $\phi$-subgaussian random variables

Krzysztof Zajkowski

For $p\ge 1$ let ${\phi }_p(x)=x^2/2$ if $|x|\le 1$ and ${\phi }_p(x)=1/p|x{|}^p-1/p+1/2$ if $|x|>1$. For a random variable $\xi$ let ${\tau }_{{\phi }_p}(\xi )$ denote $\inf\{a\ge 0:\;\forall_{λ\in\mathbb{R}}\;…