10 problems

Bessel-process strong law and central limit conjecture. We conjecture that

Consider a spatial process $X:\mathbb{R}\to\mathbb{R}$ and construct the evolving Poisson point sets $T_t$, the associated process $Y_t$, and the centered graph … where…

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…

Two-Bessel simultaneous-zero conjecture. For every $k\in\mathbb{N}$,

Dynamical transition conjecture. For all $\delta>2$, a solution to the $\delta$-Bessel SPDE almost surely hits the obstacle $0$ in at most…

Bessel SPDE extension conjecture. The natural extension of the SPDEs for $\delta>3$ and $\delta=3$ to the region $\delta<3$ should be given by the corresponding SPDEs for…

Let $X_t$ be the Bessel process with dimension parameter $d\geq 2$, characterized by the generator … For integer $d$, this equation describes the radial part of a $d$-dimensional B…

Let $X$ be a BESM$(\delta,d)$ process, as defined in the paper, with state space $E$. Strong Feller conjecture. The process $X$ is strongly Feller. This would establish an addition…

Let $X=(X_s,s\geq 0)$ be a two-dimensional Brownian motion, let $R=(R_s,s\geq 0)$ be a Bessel process of index $-\alpha$ for $\alpha>0$, and let $F$ be a suitable functional of the…