论文标题
通过汉密尔顿 - 雅各比 - 贝尔曼方程进行切换和同质化的马尔可夫过程的巨大偏差
Large deviations for Markov processes with switching and homogenisation via Hamilton-Jacobi-Bellman equations
论文作者
论文摘要
我们考虑由依赖于内部自由度的弱周期性潜力梯度驱动的扩散过程建模的分子电动机的背景。可以自由解释为分子开关的内部状态的开关被建模为马尔可夫跳跃过程，取决于电动机的位置。重新缩放空间和时间，扩散过程的轨迹的极限在周期性的电位和内部自由度上都匀浆。围绕均质的极限，我们通过冯和库尔茨开发的方法证明了轨迹的较大偏差原理，基于对相关的汉密尔顿 - 雅各比 - 贝尔曼方程的分析，并具有汉密尔顿人的汉密尔顿方程，这是一个创新的事实，取决于位置和力量。
We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be interpreted as a molecular switch, is modelled as a Markov jump process that depends on the location of the motor. Rescaling space and time, the limit of the trajectory of the diffusion process homogenizes over the periodic potential as well as over the internal degree of freedom. Around the homogenized limit, we prove the large deviation principle of trajectories with a method developed by Feng and Kurtz based on the analysis of an associated Hamilton--Jacobi--Bellman equation with an Hamiltonian that here, as an innovative fact, depends on both position and momenta.
