2016/05/11 by Chen Jia, Jia, Chen · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #Gene Regulatory Network Analysis #Graph theory and applications #Markov Chains and Monte Carlo Methods #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1605.03502
openalex publication_date 2016/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.