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
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.
Ann. Appl. Probab., Volume 26, Number 1 (2016), 45-72.
Received: May 2014
Revised: October 2014
First available in Project Euclid: 5 January 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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