Approximation of Fractional Brownian Motion by Martingales
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In this paper, the authors studied the problem of optimal approximation of a fractional Brownian motion by martingales and proved that there exists a unique martingale closest to fractional brownian motion in a specific sense.Abstract:
We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.read more
Citations
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Approximation of the Rosenblatt process by semimartingales
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TL;DR: In this article, the optimal approximation of a Rosenblatt process based on semimartingales of the form where (y1, y2)↦a(y 1, y 2) is a square integrable process and B is a standard Brownian motion was considered.
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Distance from fractional Brownian motion with associated Hurst index 0<H<1/2 to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent
TL;DR: In this article, the best approximation of the fractional Brownian motion with the Hurst index was found by Gaussian martingales of the form ∆ ∆ + ∆ − ∆, where ∆ is a Wiener process, ∆ > 0.
References
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Book
Convex analysis and minimization algorithms
TL;DR: In this article, the cutting plane algorithm is used to construct approximate subdifferentials of convex functions, and the inner construction of the subdifferential is performed by a dual form of Bundle Methods.
Book
Stochastic Calculus for Fractional Brownian Motion and Related Processes
TL;DR: In this paper, the authors integrate Wiener Integration with respect to Fractional Brownian Motion (fBm) and Statistical Inference with FBm with the objective of statistical inference.
Journal ArticleDOI
An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions
TL;DR: The Radon-Nikodym derivative between a centred fractional Brownian motion Z and the same process with constant drift is derived by finding an integral transformation which changes Z to a process with independent increments as discussed by the authors.
Journal ArticleDOI
Wavelets, Generalized White Noise and Fractional Integration: The Synthesis of Fractional Brownian Motion.
TL;DR: In this paper, an almost sure convergent expansion of fractional Brownian motion in wavelets is presented, which decorrelates the high frequencies of the high frequency corrections of the wavelet expansion.
Journal ArticleDOI
A series expansion of fractional Brownian motion
TL;DR: This paper proves the series representation where X1,X2,... and Y1,Y2,... are independent, Gaussian random variables with mean zero and and the constant cH2 is defined by cHH2=π−1Γ(1+2H) sin πH.
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