Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series A, Pt. 3, pp. 331--338

A NOTE ON WEAK-* PERTURBATIONS OF g-MEASURES

By

Y. LACROIX, Université de Picardie Jules Verne, France

SUMMARY. We observe that the standard Kemeny and Snell identity, basic in Markov Chain Perturbation Theory, generalizes to chains with complete connections. Therefrom a few elementary observations are derived for weak-* perturbation of g-measures considered as a function of g. This identity is applied to produce a simple proof for the phase transition phenomenon recently exhibited in Bramson and Kalikow (1993).

AMS (1991) subject classification. 28D05, 41A80, 47A35, 60J10, 60J35, 82B30.

Key words and phrases. Kemeny and Snell identity, chains with complete connections, local perturbations, phase transition, uniqueness.

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