Recurrent Boundary Theory
Boundary theory for recurrent chains proceeds along altogether different lines from the approach in Chapter 10. A clue to the difficulty is that every non-negative superregular function is constant, and hence the representation of such functions degenerates. Moreover, since a recurrent chain is in every state infinitely often with probability one, an almost-everywhere convergence theorem is out of the question.
KeywordsBoundary Point Independent Random Variable Representation Theorem Harmonic Measure Boundary Theory
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