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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.
Vladas Pipiras, Murad S Taqqu
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Piecewise fractional Brownian motion
IEEE Transactions on Signal Processing, 2005Starting from fractional Brownian motion (fBm) of unique parameter H, a piecewise fractional Brownian motion (pfBm) of parameters Hi, Ho and gamma is defined. This new process has two spectral regimes: It behaves like an fBm of parameter Ho for low frequencies and like an fBm of parameter Hi for high frequencies .When Ho = Hi, or for limit cases, pfBm ...
Emmanuel Perrin +3 more
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Trading Fractional Brownian Motion
SIAM Journal on Financial Mathematics, 2017The authors consider a market with an asset price described by fractional Brownian motion, which can be traded with temporary nonlinear price impact. The asymptotically optimal strategies for the maximization of expected terminal wealth are obtained.
Guasoni P, Nika Z, Rasonyi M
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Is it Brownian or fractional Brownian motion?
Economics Letters, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Meiyu, Gençay, Ramazan, Xue, Yi
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On the prediction of fractional Brownian motion
Journal of Applied Probability, 1996Integration with respect to the fractional Brownian motion Z with Hurst parameter is discussed. The predictor is represented as an integral with respect to Z, solving a weakly singular integral equation for the prediction weight function.
Gripenberg, Gustaf, Norros, Ilkka
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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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On the Maximum of a Fractional Brownian Motion
Theory of Probability & Its Applications, 2000For a fractional Brownian motion \(B_{\gamma} = \{B_{\gamma}(t), t \geq 0\}\), \(0 < \gamma < 2\), \(x > 0\) and open bounded interval \(\Delta\) containing \(0\) the following relation is proved \[ \log P \left(\sup_{t \in T\Delta} B_{\gamma}(t) < x\right) = -\log T (1+O((\log T)^{-1/2})) \text{as} T \to \infty. \] If \(\Delta = (0,1)\), then [see the
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On the spectrum of fractional Brownian motions
IEEE Transactions on Information Theory, 1989Fractional Brownian motions (FBMs) provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order. However, due to the nonstationary nature of these processes, the precise meaning of such spectra remains generally unclear.
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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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On the simulation of sub-fractional Brownian motion
2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR), 2015We present a method for numerical approximation of sample paths of the sub-fractional Brownian motion. Taking into account the main properties of the stochastic process, the main idea of this methods consists in the replacement of the process integral representation by a Riemann sum. We also give an estimate of an upper bound on the approximation error
Aneta Morozewicz, Darya V. Filatova
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