The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 1 (2016), 45-72.
A uniform law for convergence to the local times of linear fractional stable motions
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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