Can a CTMC with an absorbing state be reversible? I guess not, as the product of rates through any loop cannot be equal when the loop involves the absorbing state (Kolmogorov criterion). Is my intuition correct? Is there any way of formalising this intuition?
2026-04-24 08:07:51.1777018071
Can an absorbing CTMC be reversible?
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It's reversible with respect to the probability measure concentrated on the absorbing state.
There's a famous paper by Chung and Walsh on how to construct more sensible Markov chains that
may be considered the reversed process in this sort of situation.