5 problems

Convergence-rate conjecture. Theorem … and $$ increase with $\alpha$.

The dyadic local-time conjecture. Almost surely, $\widetilde{L}^{\pi_n}_t(x)$ converges uniformly for $(t,x)\in[0,T]\times\mathbb{R}$ to

Let $S(X_t)=\overline{\{x:X(t,x)>0\}}$ be the closed support of $X_t$, let $\partial S(X_t)$ denote its boundary, and let $L_t$ be the local-time measure associated with the bounda…

Let $v>\gamma^{\circ}$ and let $\mathbbm{Q}^{U_v}=\lim_{a\to\infty}\mathbbm{W}(\mathord\cdot\mid\mathcal{E}_a^{U_v})$ be any measure supplied by the critical-speed framework. Let…

Let $f$ satisfy … and let $\mathbb{P}$ be any weak limit of the conditioned Wiener measures $\mathbb{W}_t$. Let $L_t$ denote the local time at the origin at time $t$. Local-time se…