We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.
Duffy, James A. (2016). 'A uniform law for the convergence to local times of linear fractional stable motions'. Annals of Applied Probability. 26, 1, 45-72.