Electronic Communications in Probability

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

Ciprian Tudor

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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