I am aware that the Borel probability convergence determining classes of the metric space $(\mathbb R^\infty,d)$ where $d(x,y)=\sum_{i=1}^\infty \dfrac{\min\{|x_i-y_i|,1\}}{2^i}$ with $x=(x_1,x_2,...)$ and $y=(y_1,y_2,...)$, are the finite dimensional cylinder sets $\pi_{i_1,t_2,...,i_k}^{-1}(A)$ where $A\in\mathbb B(\mathbb R^k)$ and $\pi_{i_1,...,i_k}:\mathbb R^\infty\to\mathbb R^k$ is defined by $\pi_{i_1,...,i_k}(x)=(x_{i_1},...,x_{i_k})$.
Since $\mathbb R^\infty,d)$ is Polish, along with the fact listed above, we have that if we have a sequence of tight Borel probability measures whose finite dimensional distributions converge, we would have convergence of the entire stochastic process.
Is there any stochastic application of this result? That is, can we use this to figure out the convergence properties of some well known stochastic process?