Department of Bioinformatics and Life Science, Soongsil University, Seoul, South Korea.
J Chem Phys. 2012 Aug 21;137(7):074103. doi: 10.1063/1.4743955.
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive nth-order Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochastic model, an nth-order Markov process emerges as the unique maximum entropy solution to this otherwise underdetermined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from the first principles.
主方程，更一般地说，马尔可夫过程通常被用作随机过程的模型。它们通常基于随机化和粗粒化假设来证明。在这里，我们则将 n 阶马尔可夫过程和主方程作为反问题的唯一解来推导。我们发现，当约束不足以唯一确定随机模型时，n 阶马尔可夫过程会作为该未完全确定问题的唯一最大熵解而出现。这为证明此类模型提供了一种严格的替代方法，同时为推广通常被认为源自第一性原理的广泛接受的随机模型提供了系统的方法。
