Journal
STATISTICS & PROBABILITY LETTERS
Volume 116, Issue -, Pages 122-130Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spl.2016.04.020
Keywords
Embedding problem; Stochastic matrix; Generator estimation; Detailed balance
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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. (C) 2016 Elsevier B.V. All rights reserved.
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