A uniform law for convergence to the local times of linear fractional stable motions

James A. Duffy

doi:10.1214/14-aap1085

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arXiv · 1501.05467

A uniform law for convergence to the local times of linear fractional stable motions

James A. Duffy

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Abstract

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.

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James A. Duffy. 2016-02-01. A uniform law for convergence to the local times of linear fractional stable motions. https://doi.org/10.1214/14-aap1085

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