8 problems

Let $(x_t^n)_{t\geq 0}$ be a sequence of semimartingales whose diffusion approximation, when it exists, is a solution of an Itô equation … Here $w_t$ is a vector-valued Wiener proc…

Boundary-layer confinement conjecture. In the diffusive limit, the boundary layer becomes confined to a shrinking region near $\Gamma$, so that the influence of the precise diffusi…

Alternative diffusion-limit conjecture. The process $L^{(r)}_{\rm dif}(\cdot)$ can nevertheless weakly converge to a process other than $Z(\cdot)$.

Vanishing-threshold-mass conjecture.

Limiting-distribution conjecture. The limiting distribution is truncated exponential or uniform below the threshold level and exponential above it.

Zero-boundary extension conjecture. The two-sided local-limit conjecture also holds with the cutoff parameter set to $\epsilon=0$.

Two-sided local-limit conjecture. The conditioned discrete process converges in distribution in $D([0,t_1],\mathbb{R}^3)$ to $\xi^\star$, started at $(\delta_0,m_0,s_0)$ and condit…

Let $n$ be the host population size, let $I_h^n(t)$ denote the number of infected hosts at time $t$, and let $\mathcal{R}_0$ be the basic reproduction number. When…