The Annals of Applied Probability

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

James A. Duffy

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 1 (2016), 45-72.

Dates
Received: May 2014
Revised: October 2014
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1452003234

Digital Object Identifier
doi:10.1214/14-AAP1085

Mathematical Reviews number (MathSciNet)
MR3449313

Zentralblatt MATH identifier
1334.60044

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60G18: Self-similar processes 60J55: Local time and additive functionals
Secondary: 62G08: Nonparametric regression 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Fractional stable motion fractional Brownian motion local time weak convergence to local time integral functionals of stochastic processes nonlinear cointegration nonparametric regression

Citation

Duffy, James A. A uniform law for convergence to the local times of linear fractional stable motions. Ann. Appl. Probab. 26 (2016), no. 1, 45--72. doi:10.1214/14-AAP1085. https://projecteuclid.org/euclid.aoap/1452003234


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