# Joint law of the time integral of Brownian motion and its maximum

Suppose $W_t$ is a standard one dimensional Brownian motion. Let $M_t$ and $I_t$ be its running maximum and time integral, respectively:

$$M_t=\max_{0\leq s\leq t}\,W_s$$
$$I_t=\int\limits_0^tW_s\,\mathrm{d}s$$

The laws of $M_t$ and $I_t$ can be easily derived by any beginnner studying stochastic processes. However, I haven't seen anything in the literature about their joint law. Is the joint law of $M_t$ and $I_t$ known?

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