论文标题
动力大偏差的扩散
Dynamical large deviations of diffusions
论文作者
论文摘要
我们解决了与马尔可夫扩散的时间集成功能的波动有关的两个问题，马尔可夫扩散量，用于建模非平衡系统。首先，我们得出并说明用于获得反射扩散的电流类型可观察物的较大偏差的光谱问题上的适当边界条件。对于第二个问题，我们研究线性扩散，并获得与线性添加剂，二次添加剂和线性电流类型可观察到的生成函数的确切结果，并使用Feynman-KAC公式可观察。我们研究了这些可观察到的每一个生成函数的长期行为，以确定所谓的速率函数和有效过程的形式，负责表现出相关的可观察到的波动。发现对于这些可观察到的每一个，有效过程再次是线性扩散。我们将一般结果应用于$ \ Mathbb {r}^2 $中的各种线性扩散，尤其强调研究原始过程的密度和当前的修改方式以创造波动。
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the spectral problem used to obtain the large deviations of current-type observables for reflected diffusions. For the second problem we study linear diffusions and obtain exact results for the generating function associated with linear additive, quadratic additive and linear current-type observables by using the Feynman-Kac formula. We investigate the long-time behavior of the generating function for each of these observables to determine both the so-called rate function and the form of the effective process responsible for manifesting the fluctuations of the associated observable. It is found that for each of these observables, the effective process is again a linear diffusion. We apply our general results for a variety of linear diffusions in $\mathbb{R}^2$, with particular emphasis on investigating the manner in which the density and current of the original process are modified in order to create fluctuations.
