We prove functional limit laws for the increment functions of empirical processes based upon randomly right-censored data. The increment sizes we consider are classified into different classes covering the whole possible spectrum. We apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions. In particular, we treat the case of kernel density and hazard rate estimators.
"Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications." Ann. Probab. 28 (3) 1301 - 1335, July 2000. https://doi.org/10.1214/aop/1019160336