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ABSTRACT. In [4], S. Elaydi obtained a characterization of the stability of the null solution of the Volterra difference equationby localizing the roots of its characteristic equationThe assumption that (a n ) ∈ 1 was the single hypothesis considered for the validity of that characterization, which is an insufficient condition if the ratio R of convergence of the power series of the previous equation equals one. In fact, when R = 1, this characterization conflicts with a result obtained by Erdös et al. in [8]. Here, we analyze the R = 1 case and show that some parts of that characterization still hold. Furthermore, studies on stability for the R < 1 case are presented. Finally, we study some results related to stability via finite approximation.

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