Electronic Communications in Probability

Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Ciprian Tudor

Full-text: Open access

Abstract

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 28, 278-289.

Dates
Accepted: 9 July 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234737

Digital Object Identifier
doi:10.1214/ECP.v14-1481

Mathematical Reviews number (MathSciNet)
MR2524979

Zentralblatt MATH identifier
1189.60085

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60H05: Stochastic integrals 60F05: Central limit and other weak theorems 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
multiple stochastic integrals selfsimilar processes fractional Brownian motion Hermite processes limit theorems Stein's method

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Tudor, Ciprian. Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion. Electron. Commun. Probab. 14 (2009), paper no. 28, 278--289. doi:10.1214/ECP.v14-1481. https://projecteuclid.org/euclid.ecp/1465234737


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