4 problems

Optimality of the exponent one-half in convergence rates for dynamic random Hamilton–Jacobi equations
Consider the setting of Theorems --, with the convergence rates established there. Optimality conjecture. The convergence rates obtained therein are optimal up to slowly varying fa…
openergodicity hamilton-jacobi-equations random-environments
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05
Anderson–Kim's ergodicity conjecture for weakly reversible stochastic mass-action reaction systems
A stochastic mass-action reaction system (SMART) is a continuous-time Markov chain describing molecule counts in a mass-action reaction network, and it is weakly reversible when ev…
openergodicity reaction-networks stochastic-processes
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09
One Force -- One Solution principle for the open KPZ equation
Fix $u,v\in\R$ . Let $h_0,\tilde h_0\in\operatorname{C}([0,1])$ be arbitrary random functions on the same probability space, and let $\xi$ be white noise on $\mathbb{R}\times[0,1]$ .…
openergodicity kpz-equation stochastic-processes
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02
The order-1/d exponential ergodicity conjecture for generalized reflected Brownian motion
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…
openergodicity reflected-brownian-motion stochastic-processes
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07

Optimality of the exponent one-half in convergence rates for dynamic random Hamilton–Jacobi equations