This paper addresses the almost sure convergence and the asymptotic normality of an estimator of the multidimensional renewal function based on random fields. The estimator is based on a sequence of non-negative independent and identically distributed (i.i.d.) multidimensional random fields and is expressed as infinite sums of k-folds convolutions of the empirical distribution function. It is an extension of the work from the case of the two-dimensional random fields to the case of the d-dimensional random fields where d>2. This is established by the definition of a “strict order relation”. Concrete applications are given.