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

Preprint English OPEN
Zajkowski, Krzysztof;
(2016)
  • Subject: 60F15 | Mathematics - Probability

For $p\ge 1$ let $\varphi_p(x)=x^2/2$ if $|x|\le 1$ and $\varphi_p(x)=1/p|x|^p-1/p+1/2$ if $|x|>1$. For a random variable $\xi$ let $\tau_{\varphi_p}(\xi)$ denote $\inf\{a\ge 0:\;\forall_{\lambda\in\mathbb{R}}\; \ln\mathbb{E}\exp(\lambda\xi)\le\varphi_p(a\lambda)\}$; $\... View more
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