Counterexample in Kolmogorov theorem about existence of almost surely continuous modification

Question

I want to understand this Kolmogorov theorem about existence of almost surely continuous modification:
A process $\{\xi_t, \in[0,T]\}$ admits an almost surely continuous modification if there exist constants $a,b,c>0$ such that $$\mathbb{E}[|\xi_t-\xi_s|^a]\leq b|t-s|^{1+c}$$ for all $s,t\in [0,T]$.
And I have such a question. What if we take a process $\{\xi_t=e^{w_t^3}, t\in[0,T]\}$, where $w_t$ is standard wiener process. Then will it be determined $\mathbb{E}[|\xi_t-\xi_s|^a]$ ?