6 problems

Let $\operatorname{GRBM}(R,\mu,\Gamma,U)$ be the generalized reflected Brownian motion defined by the strong solution of the stochastic differential equation in the paper, with tra…

Let $u^R(t,x,y):=\mathbb{P}_y(M^R_t\leq x)$, where $\mathbb{P}_y$ is the law of branching reflected Brownian motion starting at $y\geq 0$. Let $q^R_{\delta}(y,t)$ be defined as in…

General large deviations principle. For every measurable $A\subset\mathbb{R}^d_+$,

Lagrangian measure convergence conjecture. The measures ${\bf Q}_{r,t}$ converge to a random measure ${\bf Q}_r$ on $D_1\setminus{\mathcal B}(0,r)$ as $t\to\infty$, in the sense of…

Many-hole domain conjecture. If $k$ is sufficiently large and

Stationary distribution conjecture. If $d=3$, then there is $r_0>0$ such that for $r\leq r_0$, the process $(X,Y)$ has a stationary distribution $Q$ which does not charge the diago…