Let $X=\lbrace X_t \rbrace_{t\geq 0}$ be a process satisfying the following condition$\colon$ For all $T>0$ there exist positive constants $\alpha$ , $\beta$ , $D$ such that $$ E[|X_t-X_s|^{\alpha}]\leq D|t-s|^{1+\beta} \,\,\ 0\leq s, t\leq T.$$
Then there exists a continuous modification of $X$ .