2 problems

Bessel coupling conjecture. There exists a coupling of $(R,Y)$ and $\widetilde{\mathbf{B}}$ such that almost surely there are $\delta_1>0$ and $n_1\in\mathbb{N}$ for which, for eve…

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…