Variational and optimal control representations of conditioned and driven processes
Variational and optimal control representations of conditioned and driven processes
复制标题
条件和驱动过程的变分和最优控制表示
DOI：
10.1088/1742-5468/2015/12/p12001
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
H. Touchette
中科院分区：
文献类型：
--
作者：
R. Chetrite;H. Touchette
我们最近表明，马尔可夫过程的条件下，涉及时间积分随机变量的罕见事件可以描述在长时间限制的有效马尔可夫过程，称为驱动过程，这是数学上给出的Doob的h-变换的推广。我们在这里表明，这个驱动过程可以表示在其他两种方式：第一，作为一个过程，满足各种变分原理，涉及大偏差函数和相对熵，第二，作为一个最优的随机控制过程，最小化成本函数也相关的大偏差函数。这些解释的驱动过程推广和统一了许多以前的结果最大熵方法的非平衡系统，正算子的谱特征，和控制方法的大偏差理论。他们还导致，简要讨论，新的方法分析或数值逼近大偏差函数。
We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given mathematically by a generalization of Doob’s h-transform. We show here that this driven process can be represented in two other ways: first, as a process satisfying various variational principles involving large deviation functions and relative entropies and, second, as an optimal stochastic control process minimizing a cost function also related to large deviation functions. These interpretations of the driven process generalize and unify many previous results on maximum entropy approaches to nonequilibrium systems, spectral characterizations of positive operators, and control approaches to large deviation theory. They also lead, as briefly discussed, to new methods for analytically or numerically approximating large deviation functions.