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Deconvolution of fractional brownian motion
Journal of Time Series Analysis, 2002We show that a fractional Brownian motion with H′∈(0,1) can be represented as an explicit transformation of a fractional Brownian motion with index H ∈(0,1). In particular, when H′=½, we obtain a deconvolution formula (or autoregressive representation) for fractional Brownian motion.
Pipiras, Vladas, Taqqu, Murad S.
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The fractional mixed fractional Brownian motion
Statistics & Probability Letters, 2003Let \(B_1\) and \(B_2\) be two independent fractional Brownian motions of Hurst index \(H_1\) and \(H_2\), respectively. Given real numbers \(\lambda_1\) and \(\lambda_2\), the two-parameter process \(Z\) is defined by \[ Z(w,s):= \lambda_1\,s^{H_2}\,B_1(w) + \lambda_2\,s^{H_1}\,B_2(w),\quad 0\leq w\leq s.
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Tempered fractional Brownian motion
Statistics & Probability Letters, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Meerschaert, Mark M., Sabzikar, Farzad
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Approximations for reflected fractional Brownian motion
Physical Review E, 2019Fractional Brownian motion is a widely used stochastic process that is particularly suited to model anomalous diffusion. We focus on capturing the mean and variance of fractional Brownian motion reflected at level 0. As explicit expressions or numerical techniques are not available, we base our analysis on Monte Carlo simulation.
Malsagov, A., Mandjes, M.
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Spectral correlations of fractional Brownian motion
Physical Review E, 2006Fractional Brownian motion (fBm) is a ubiquitous nonstationary model for many physical processes with power-law time-averaged spectra. In this paper, we exploit the nonstationarity to derive the full spectral correlation structure of fBm. Starting from the time-varying correlation function, we derive two different time-frequency spectral correlation ...
Tor Arne, Øigård +2 more
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Fractal (fractional) Brownian motion
WIREs Computational Statistics, 2011AbstractFractal Brownian motion, also called fractional Brownian motion (fBm), is a class of stochastic processes characterized by a single parameter called the Hurst parameter, which is a real number between zero and one. fBm becomes ordinary standard Brownian motion when the parameter has the value of one‐half. In this manner, it generalizes ordinary
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On Fractional Brownian Motion and Wavelets
Complex Analysis and Operator Theory, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Albeverio, S. +2 more
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Statistical Inference with Fractional Brownian Motion
Statistical Inference for Stochastic Processes, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kukush, Alexander +2 more
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Fractional Brownian motion and Martingale-differences
Statistics & Probability Letters, 2004Let \((\xi^{(n)})_{n\geq1}\) be a sequence of square integrable martingale-differences such that for all \(i\geq1\), \(\lim_{n\to\infty}n(\xi_{i}^{(n)})^2=1\) a.s. and for some \(C\geq1\), \(\max_{1\leq i\leq n}|\xi_{i}^{(n)}|\leq C/\sqrt n\) a.s. Let us define \(W_{t}^{n}:=\sum_{i=1}^{[nt]}\xi_{i}^{(n)}\), \(0\leq t\leq1\), and \(Z_{t}^{n}:=\int_{0 ...
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Fractional Brownian motion via fractional Laplacian
Statistics & Probability Letters, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bojdecki, Tomasz, Gorostiza, Luis G.
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