Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields

“…Ref. [3] generalized the results of ref. [2] by introducing the multidimensionalmultivariate renewal function and its estimator with an appropriate Skorohod topology.…”

Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields

“…Harel and Ravelomanantsoa [20] show not only almost sure convergence and asymptotic normality but also weak convergence on Skorohod topology of the estimator. In the two-dimensional and bivariate case, Harel et al [21] study almost sure convergence and asymptotic normality of the estimator while, in the multidimensional and multivariate case, Harel et al [22] prove the weak convergence on Skorohod topology of the estimator. Andriamampionona et al [23] study the asymptotic normality of the renewal function estimator for sequences of random fields in dimension 2.…”