Occupation time problem for multifractional Brownian motion

DOI10.19195/0208-4147.39.1.7zbMath1486.60065OpenAlexW3011127539MaRDI QIDQ5227570

Mohamed Ait Ouahra, Aissa Sghir, Hanae Ouahhabi, Raby Guerbaz

Publication date: 6 August 2019

Published in: Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.19195/0208-4147.39.1.7

zbMATH Keywords

fractional Brownian motionlimit theoremlocal timemultifractional Brownian motionfractional derivativelocal asymptotic self-similarity

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Local time and additive functionals (60J55) (L^p)-limit theorems (60F25)

Cites Work

• Local times of multifractional Brownian sheets
• Limit theorems and variation properties for fractional derivatives of the local time of a stable process
• Limit theorems for certain functionals associated to stable processes in a Hölder space
• Elliptic Gaussian random processes
• Limit theorems for local times of fractional Brownian motions and some other self-similar processes
• On some limit theorems for occupation times of one dimensional Brownian motion and its continuous additive functionals locally of zero energy
• Chaotic expansion and smoothness of some functionals of the fractional Brownian motion
• Sample path properties of the local time of multifractional Brownian motion
• Weak convergence to fractional Brownian motion in some anisotropic Besov space
• Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion
• Occupation time problems for fractional Brownian motion and some other self-similar processes
• On the local time of multifractional Brownian motion
• A decomposition of additive functionals of finite energy
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