Conditioned local limit theorems for random walks defined on finite Markov chains

Let ( X n ) n ⩾ 0 be a Markov chain with values in a finite state space X starting at X 0 = x ∈ X and let f be a real function defined on X . Set S n = ∑ k = 1 n f ( X k ) , n ⩾ 1 . For any y ∈ R denote by τ y the first time when y + S n becomes non-positive. We study the asymptotic behaviour of the...

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