Show that there exists a stochastic process \(\left(X_{t}ight)_{t \geqslant 0}\) such that the random variables \(X_{t}\) are independent \(\mathrm{N}(0, t)\) random variables. This process also satisfies \(\mathbb{P}\left(\lim _{s ightarrow t} X_{S}ight.\) exists \()=0\) for every \(t>0\).