The Nonlocal Inverse Problem of Donsker and Varadhan

Donsker-Varadhan 大偏差原理用于局部阻尼和随机强迫非线性薛定谔方程

Donsker-Varadhan large deviation principle for locally damped and randomly forced NLS equations

本文提出了一种新的抽象准则，用于研究局部阻尼和随机强迫非线性薛定谔方程的大偏差原理，并应用于波动方程和纳维-斯托克斯系统。

A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue

The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $Ω$ by the largest mean first exit time of the associated drift-diffusion process via $$λ_1 \geq \frac{1}{\sup_{x \in Ω} \mathbb{E}_x τ_{Ω^c}}.$$ Instead of looking at the mean of the first exit time, we study quantiles: let $d_{p, \partial Ω}:Ω\rightarrow \mathbb{R}_{\geq 0}$ be the smallest time $t$ such that the likelihood of exiting within that time is $p$, then $$λ_1 \geq \frac{\log{(1/p)}}{\sup_{x \in…

有界区域中白噪声驱动二维Navier-Stokes系统的三级大偏差

Level-3 large deviations for the white-forced 2D Navier-Stokes system in a bounded domain

该研究针对有界区域白噪声驱动的Navier-Stokes系统，在噪声非退化假设下，借助改进的Kifer准则等多种方法建立了Donsker-Varadhan型的二级与三级大偏差原理，给出了对应速率函数。

The Dirichlet problem for the Bellman equation at resonance

We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and positively homogeneous. Examples of such operators include the Hamilon-Jacobi-Bellman operator and the Pucci extremal operators. In the case that the two principal half-eigenvalues are not equal, we show that the measures which achieve the minimum in this formula provide a partial characterization of the solvability of the corresponding Dirichlet problem at res…