Convergence faible vers une classe de processus Gaussiens en norme de Besov anisotropique

Boufoussi, Brahim; Guerbaz, Raby

doi:10.1016/j.bulsci.2006.01.003

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Weak Limit Theorem Based On Donsker Kernels1

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“…Boufoussi and Guerbaz [5] proved an approximation result of Donsker's type for a class of two parameter Gaussian processes in anisotropic Besov spaces. It seems reasonable to prove Theorem 3.1 by their results.…”

Section: Weak Limit Theorem Based On Donsker Kernelsmentioning

confidence: 99%

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Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces

Dai

2011

J. Appl. Math. Comput.

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We study the weak convergence of the family of processes {V n (t)} n∈N defined bywhere {θ n (u)} n∈N is a family of processes converging in law to a Brownian motion, as n → ∞. We consider two cases of {θ n }. First, we construct θ n based on the wellknown Donsker's theorem and show that {V n (t)} n∈N converges in law to a multifractional Brownian motion of Riemann-Liouville type, as n → ∞. Second, we construct θ n based on a Poisson process, and then show that a multifractional Brownian motion of Riemann-Liouville type can be approximated in law by {V n (t)} n∈N .

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Section: Weak Limit Theorem Based On Donsker Kernelsmentioning

confidence: 99%

“…The author thanks the department for good working condition. The author also would like to thank the referees for helpful comments to improve this work and bringing the paper of Boufoussi and Guerbaz [5] to my attention. This work was also supported by the Scientific Research Foundation of Guangxi University (No.…”

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confidence: 97%