3 problems

Let $(B_t\colon t\in\mathbb{R})$ be a two-sided Brownian motion, and let $T$ be an unbiased shift embedding a probability measure orthogonal to the initial distribution. The shift…

Let $T$ be an unbiased shift such that $T\geq 0$, $\mathbb{P}_0\{B_T=0\}=1$, and $\mathbb{P}_0\{T>0\}>0$. The square-root moment conjecture. One has … This would strengthen the cor…

Let $B$ be the two-sided Brownian motion and let $T$ be an unbiased shift embedding a measure $\nu\ne\delta_0$, where $T$ need not be a stopping time or nonnegative. The fourth-mom…