Conjecture on the range and rate of convergence for the sticky-diffusion approximation

The paper considers the parameter $\alpha\in(0,1)$ in the approximation of the local time of a sticky diffusion. Theorem

$$concerns the convergence of the statistics in$$

and

$$. **Convergence-rate conjecture.** Theorem$$

holds for every $\alpha\in(0,1)$, and the rates of convergence of both

$$and$$

increase with $\alpha$.

The simulations suggest that the convergence result extends to values of $\alpha$ in $[1/2,1)$, which are not covered by the stated theorem. The conjectured dependence of the convergence rate on $\alpha$ remains unestablished in the supplied text.