Let (left(B_{t}ight)_{t geqslant 0}) be a real-valued stochastic process with exclusively continuous sample paths. Assume that (left(B_{q}ight)_{q

Question:

Let $\left(B_{t}ight)_{t \geqslant 0}$ be a real-valued stochastic process with exclusively continuous sample paths. Assume that $\left(B_{q}ight)_{q \in \mathbb{Q} \cap[0, \infty)}$ satisfies (B0)-(B3). Show that $\left(B_{t}ight)_{t \geqslant 0}$ is a BM.

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