Summary: Let \(\{X(t,\omega):t\in\mathbb{R}^N\}\) be a stochastic process taking values in \(\mathbb{R}^d\) and with its paths continuous, with the condition: let \(0<\alpha<1\), \(M>0\), \(\beta\geq d\) be constants such that \(E|X(t)-X(s)|^\beta\leq M|t-s |^{\alpha\beta}\), \(t,s\in\mathbb{R}^N\), \((\beta>\frac{N} {\alpha})\) or \(E\sup_{h\in[0, T]^N}|X(t+h)-X(t)|^\beta\leq MT^{\alpha \beta}\), \(t\in\mathbb{R}^N\), \(0<T\leq 1\). We obtain the best upper bounds of Hausdorff dimension of the image set, the graph sets and the level sets about \(X\) for the Borel sets, moreover, with the condition: let \(a,\alpha, d>0\) be constants such that \(P(|X(t)-X(s)|\leq|t-s |^\alpha x)\leq ax^d\), \(t,s\in\mathbb{R}^N\), \(x\geq 0\). We obtain the best lower bounds of Hausdorff dimension of the image set, the graph sets about \(X\) for the Borel sets.