Given $\{X_{n},\mathcal{F}_{n}\}$ is an adapted process satisfying the following conditions:
$X_{n}>0,\ \forall\ n>0.$
There exists $ \epsilon>0,\ \sigma>0,$ such that $\mathbb{E}(X_{n}^{2+\epsilon}|\mathcal{F}_{n-1})\le \sigma.$
$\sum_{k=1}^{n}X^{2}_{k}\rightarrow+\infty\ a.s..$
Then can we acquire $\lim_{n\rightarrow+\infty}\frac{X_{n}}{\sqrt{\sum_{k=1}^{n}X_{k}^{2}}}=0\ \ a.s.?$
