2 problems

Let $B$ be a one-dimensional Brownian motion on $[0,\infty)$ and let $K$ be its almost surely existing concave majorant on $[0,\infty)$. Ouaki–Pitman conjecture. The process $2K-B$ h…

Let $B=(B_t)_{t\geq 0}$ be a standard one-dimensional Brownian motion, and let $K=(K_t)_{t\geq 0}$ be its almost surely unique concave majorant on $[0,\infty)$. Write $R_5$ for a f…