Kolmogorov’s continuity theorem

Let $X={\{X_t\}}_{t\ge 0}$ be a process satisfying the following condition$:$For all $T>0$ there exist positive constants $\alpha$, $\beta$, $D$ such that

$$E[{|X_t-X_s|}^{\alpha }]\le D{|t-s|}^{1+\beta }\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.25em}0}\le s,t\le T.$$

Then there exists a continuous modification of $X$.