We consider the problem of testing the identity of a reversible Markov chain against a reference from a single trajectory of observations. Employing the recently introduced notion of a lumping-congruent Markov embedding, we show that, at least in a mildly restricted setting, testing identity to a reversible chain reduces to testing to a symmetric chain over a larger state space and recover state-of-the-art sample complexity for the problem.

翻译：我们考虑从单条观测轨迹检验可逆马尔可夫链与参考链恒等性的问题。通过应用最近引入的“凝聚同构马尔可夫嵌入”概念，我们证明，至少在弱约束条件下，检验可逆链的恒等性可归结为在更大状态空间上检验对称链的恒等性，并恢复了该问题当前最优的样本复杂度。