If $X=(X_t)_{t \geq 0}$ is a one-dimensional Gaussian real process I know that it means that $$ (X_{t_1}, X_{t_2}, \ldots , X_{t_n}) $$ has $n$-dimensional Gaussian distribution for any $0 \leq t_i< t_{i+1}$ for $i=1,2,....,n-1$ and $n \geq 1$. What if $(X,Y)$ is a two-dimensional Gaussian process. Does it mean that $$ (X_{t_1}, X_{t_2}, \ldots , X_{t_n}, Y_{t_1}, Y_{t_2}, \ldots , Y_{t_n}) $$ has $2n$-dimensional Gaussian distribution for any $0 \leq t_i< t_{i+1}$ for $i=1,2,....,n-1$ and $n \geq 1$?
Note An answer is given in the post Definition of a $\mathbb{R}^d$-valued Gaussian process.