Abstract
Let X 1, X 2,… be an irreducible Markov chain taking values in a measurable space (S, S), \(u:{S^2} \to {\mathbb{R}^d},{U_n} = \sum {_{i = 1}^n} u({X_i},{X_{i + 1}}),C \subset {\mathbb{R}^d}\) open and convex. Then conditioned on {U n ∈ nC} (and under some hypotheses on {X n }), it is shown that {X n } converges to a Markov chain, whose transition mechanism is specified.
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Meda, A., Ney, P. (1999). The Gibbs Conditioning Principle for Markov Chains. In: Bramson, M., Durrett, R. (eds) Perplexing Problems in Probability. Progress in Probability, vol 44. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2168-5_21
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DOI: https://doi.org/10.1007/978-1-4612-2168-5_21
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