A solution to the reversible embedding problem for finite Markov chains

作者：Jia Chen^*

来源：Statistics & Probability Letters, 2016, 116: 122-130.

DOI：10.1016/j.spl.2016.04.020

• Embedding problem
• Stochastic matrix
• Generator estimation
• Detailed balance

The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which has a deep physical and biochemical background and provide a complete solution to this new problem. We prove that the reversible embedding of a stochastic matrix, if it exists, must be unique. Moreover, we obtain the sufficient and necessary conditions for the existence of the reversible embedding and provide an effective method to compute the reversible embedding. Some examples are also given to illustrate the main results of this paper.

• 出版日期2016-9
• 单位北京计算科学研究中心