On the use of a discrete form of the Ito formula in the article 'Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations' (vol 15, pg 71, 2012)
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In the original article [LMS J.Comput. Math. 15 (2012) 7183], the authors use a discrete form of the It formula, developed by Appleby, Berkolaiko and Rodkina [Stochastics 81 (2009) no. 2, 99127], to show that the almost sure asymptotic stability of a particular two-dimensional test system is preserved whenthe discretisation step size is small. In this Corrigendum, we identify an implicit assumption in theoriginal proof of the discrete It formula that, left unaddressed, would preclude its application to the test system of interest. We resolve this problem by reproving the relevant part of the discrete It formula in such a way that confirms its applicability to our test equation. Thus, we reaffirm the main results and conclusions of the original article.
