Abstract
This article is divided into two parts: in the first we give some results about renewal and normality of a recurrent random walk (r.w.) on an abelian group, without the Harris hypothesis, which will extend the theorems of S.C. Port and C.J. Stone ([8]) to a larger class of functions. They are stated in the Theorems 1.14 and 1.15. The technique will be to approximate the recurrent r.w. by a Harris recurrent r.w., for which the recent results of A. Brunel and D. Revuz ([2–4]) hold.
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