Central limit theorem for an additive functional of the fractional Brownian motion

DOI10.1214/12-AOP825zbMath1294.60042arXiv1111.4419MaRDI QIDQ2438748

David Nualart, Fangjun Xu, Yaozhong Hu

Publication date: 6 March 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4419

zbMATH Keywords

fractional Brownian motioncentral limit theoremlocal timemethod of moments

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Local time and additive functionals (60J55)

Related Items (13)

A first-order limit law for functionals of two independent fractional Brownian motions in the critical case ⋮ Limit theorems related to the integral functionals of one dimensional fractional Brownian motion ⋮ Limit theorems for additive functionals of the fractional Brownian motion ⋮ Central limit theorem for functionals of two independent fractional Brownian motions ⋮ On the local times of noise reinforced Bessel processes ⋮ Approximation of fractional local times: zero energy and derivatives ⋮ Temporal asymptotics for fractional parabolic Anderson model ⋮ Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes ⋮ Second-order limit laws for occupation times of fractional Brownian motion ⋮ Nonlocal stochastic integro-differential equations driven by fractional Brownian motion ⋮ Stochastic partial differential equations with gradient driven by space-time fractional noises ⋮ Homogenization Driven by a Fractional Brownian Motion: The Shear Layer Case ⋮ On \(L^{2}\) modulus of continuity of Brownian local times and Riesz potentials

Cites Work

• The weak stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6
• Central limit theorems for multiple Skorokhod integrals
• Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case \(H=1/4\)
• Integral representation of renormalized self-intersection local times
• Occupation densities
• A limit theorem for occupation times of fractional Brownian motion
• Renormalized self-intersection local time for fractional Brownian motion
• On limit processes for a class of additive functional of recurrent diffusion processes
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Ergodic Property of the Brownian Motion Process
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