I am interested in the distribution of $Z(t) = \max\{B(t),m\}$ where $B(t)$ is a standard Brownian motion and $m$ is a constant. By distribution, I mean the distribution of $Z(t)$ for a given $t$. I tried some keywords to do a search but I am not even sure what it would be called.
Any direction on it would be appreciated. I am not sure where I should start and if there is any work done on the distribution of $Z(t)$.