4 problems

General convergence conjecture. The process $\Pi^\epsilon \circ Z^\epsilon$ converges weakly to $\bar{Z}$ in $C([0,\infty);\Gamma)$, uniformly with respect to the initial condition…

Let $B(0,1)\subset\mathbb{R}^d$ be the unit ball. Let $\lambda\in C^\infty(\overline{B(0,1)})$ satisfy $\lambda>0$ on $\overline{B(0,1)}$, and let…

The stochastic diffusive behavior conjecture. For a generic perturbation $\varepsilon H_1(\cdot)$, there are smooth functions $b(I)$ and $\sigma(I)>0$, depending only on $H_1$ and…

Stronger converse conjecture. Then $\pi$ is a nonnegative measure and consequently it is a stationary distribution of $X$.