Let $(B_t)_{t\geq 0}$ be standard Brownian motion, and let $S_t := \sup_{s\leq t} B_t$ be its running maximum. Using the reflection principle, it is easy to find the joint distribution function of $(B_t, S_t)$ by considering the probability $\mathbb{P}(B_t \leq x, S_t \geq y)$. I was wondering if this result can be generalized. More specific, I was wondering if the joint distribution of $(B_0, B_1, \ldots, B_n, S_n)$ is known for $n \in \mathbb{N}$.
A reference to where I can find such a result would suffice. Similar results, e.g. the joint distribution of $(B_{t_0}, B_{t_1}, \ldots, B_{t_n}, S_{t_n})$ for some predetermined sequence $(t_n)_{n\in\mathbb{N}}$, or for the minimum instead of the maximum, are fine as well.