Let \(\mu\) be a probability measure on \(\left(\mathbb{R}^{d}, \mathscr{B}\left(\mathbb{R}^{d}ight)ight), v \in \mathbb{R}^{d}\) and consider the \(d\) dimensional stochastic process \(X_{t}(\omega):=\omega+t v, t \geqslant 0\), on the probability space \(\left(\mathbb{R}^{d}, \mathscr{B}\left(\mathbb{R}^{d}ight), \muight)\). Give an interpretation of \(X_{t}\) if \(\mu=\delta_{x}\) for some \(x \in \mathbb{R}^{d}\) and determine the family of finite dimensional distributions of \(\left(X_{t}ight)_{t \geqslant 0}\).