NDLI: Stationary Wong–Zakai Approximation of Fractional Brownian Motion and Stochastic Differential Equations with Noise Perturbations

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Stationary Wong–Zakai Approximation of Fractional Brownian Motion and Stochastic Differential Equations with Noise Perturbations

Content Provider	MDPI
Author	Viitasaari, Lauri Zeng, Caibin
Copyright Year	2022
Description	In this article, we introduce a Wong–Zakai type stationary approximation to the fractional Brownian motions and provide a sharp rate of convergence in $Lp(Ω)$ . Our stationary approximation is suitable for all values of $H\in(0,1)$ . As an application, we consider stochastic differential equations driven by a fractional Brownian motion with $H>1/2$ . We provide sharp rate of convergence in a certain fractional-type Sobolev space of the approximation, which in turn provides rate of convergence for the solution of the approximated equation. This generalises some existing results in the literature concerning approximation of the noise and the convergence of corresponding solutions.
Starting Page	303
e-ISSN	25043110
DOI	10.3390/fractalfract6060303
Journal	Fractal and Fractional
Issue Number	6
Volume Number	6
Language	English
Publisher	MDPI
Publisher Date	2022-05-30
Access Restriction	Open
Subject Keyword	Fractal and Fractional Mathematical Physics Fractional Brownian Motion Stochastic Differential Equation Wong–zakai Approximation
Content Type	Text
Resource Type	Article

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