Can anyone help me how I show the following:
Assume $Y_t-Y_s \sim N(0, \sigma^2 (t-s))$ for all $0 \leq s < t$. Then for all $n \in \mathbb{N}$ there exists a constant $c_n$ (not depending on $s$ and $t$) such that $\mathbb{E} \left[ |Y_t -Y_s|^{2n} \right] = c_n \sigma^{2n} |t-s|^n$ for $\forall s,t \geq 0$.
The question is how I find such a $c_n$.