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Article Dans Une Revue Annals of Probability Année : 2018

Limit Theorems for Markov Walks Conditioned to Stay Positive Under a Spectral Gap Assumption

Résumé

Consider a Markov chain (X n) n0 with values in the state space X. Let f be a real function on X and set S 0 = 0, S n = f (X 1) + · · · + f (X n), n 1. Let P x be the probability measure generated by the Markov chain starting at X 0 = x. For a starting point y ∈ R denote by τ y the first moment when the Markov walk (y + S n) n1 becomes non-positive. Under the condition that S n has zero drift, we find the asymptotics of the probability P x (τ y > n) and of the conditional law P x (y + S n · √ n | τ y > n) as n → +∞.

Dates et versions

hal-01706547 , version 1 (12-02-2018)

Identifiants

Citer

Ion Grama, Ronan Lauvergnat, Emile Le Page. Limit Theorems for Markov Walks Conditioned to Stay Positive Under a Spectral Gap Assumption. Annals of Probability, 2018, 46 (4), pp.1807-1877. ⟨10.1214/17-AOP1197⟩. ⟨hal-01706547⟩
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