Let $A\subset\mathbb{R}^n$ be an bounded open convex connected set (possibly with some regularity assumptions).

Now we consider $B_1$ to be a Brownian motion conditioned to stay in $A$ and $B_2$ a Brownian motion reflected on the boundary of $A$.

Is it true that $B_1$ is **"better concentrated"** than $B_2$?

This vague statement seems to be intuitively appealing (at least for me :)).

I have a few ideas how to formalize "better concentrated" but since I cannot prove (or refute) any of them I prefer to leave it unspecified. I would happy to see any "descent" notion here.