la série des probabilités de transition est une constante, elle est donc divergente. Alors, d'après le lemme de Borel-Cantelli, quand la somme des probabilités d'apparition des termes d'une suite est infinie, tous lesétatslesétats sont visités avec une probabilité de 1. En particulier, on passera dans le sous-ensemble desétatsdesétats absorbants. On peut donc ,
en ajoutant une hypothèse peu contraignante sur la fonction p m (t), nous allons pouvoir appliquer le même raisonnement ,
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