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In our monograph with B. Roynette and M. Yor, we construct a sigma-finitemeasure related to penalisations of different stochastic processes, includingthe Brownian motion in dimension 1 or 2, and a large class of lineardiffusions. In the last chapter of the monograph, we define similar measuresfrom recurrent Markov chains satisfying some technical conditions. In thepresent paper, we give a classification of these measures, in function of theminimal Martin boundary of the Markov chain considered at the beginning. Weapply this classification to the examples considered at the end of ourmonograph.

On sigma-finite measures related to the Martin boundary of recurrent Markov chains