= Solution
A <continuous-time Markov chain> is <irreducible Markov chain>[irreducible] if every state can reach every other state with positive probability. A state $i$ is <recurrent state>[recurrent] if, after leaving $i$, the chain returns to $i$ <almost surely>[with probability one]; an irreducible chain is recurrent if one, and hence every, state is recurrent. A recurrent state is <positive recurrent state>[positive recurrent] if its expected continuous <first return time> is finite, and an irreducible chain is positive recurrent when all its states are.
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