4 problems

Continuity conjecture. The map

Let $\bm X^P$ be the continuous-time particle-system approximation and let $Z(t)$ be the true solution of the corresponding McKean–Vlasov equation. Let…

Let $g:\mathbb{R}\to\mathbb{R}$ be smooth with bounded derivatives, let $G^P(x)=\frac{1}{P}\sum_{j=1}^P g(x_j)$, and let $\bm X_N^P$ be a realization of the particle system with co…

Global uniqueness conjecture. Solutions satisfying the physical jump condition are unique. Between jump times, the solution is continuously differentiable, and for every $t_0>0$ wi…