I'm wondering how to get brownian bridge's maximum and minimum's joint distribution.Brownian bridge's definition is as below.
$B_t = W_t - tW_1$ for $t \in [0,1]$, W is wiener process
How to get it? In fact, I didn't get maximum's distribution of brownian bridge. I cannot catch any idea.. I tried to get this distribution via conditional probability, that fix $W_1$, but it is still hard one. Can you help me?
edit) I think that it is concerned with joint distribution of brownian motion's maximum and minimum, and W(1). Then how to attain this one?