Results 301 to 310 of about 37,570 (330)
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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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Is it Brownian or fractional Brownian motion?
Economics Letters, 2016Abstract Fractional Brownian motion embeds Brownian motion as a special case and offers more flexible diffusion component for pricing models. We propose test statistics based on bi-power variation for testing Brownian motion against fractional Brownian motion alternatives.
Yi Xue, Meiyu Li, Ramazan Gençay
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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 ...
Perrin, Emmanuel +3 more
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Trading Fractional Brownian Motion
SIAM Journal on Financial Mathematics, 2017In a market with an asset price described by fractional Brownian motion, which can be traded with temporary nonlinear price impact, we find asymptotically optimal strategies for the maximization of expected terminal wealth. Exploiting the autocorrelation in increments while limiting trading costs, these strategies generate an average terminal wealth ...
Zsolt Nika +3 more
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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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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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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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Stochastic Analysis of the Fractional Brownian Motion
Potential Analysis, 1999Since the fractional Brownian motion (fBm) is not a semimartingale, the usual stochastic calculus cannot be used to analyze it; however since it is a Gaussian process, the authors have applied the stochastic calculus of variations which is valid on general Wiener spaces.
Ali Süleyman Üstünel +1 more
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Fractional Brownian motion via fractional Laplacian
Statistics & Probability Letters, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luis G. Gorostiza, Tomasz Bojdecki
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A Note on the Fractional Integrated Fractional Brownian Motion
Acta Applicandae Mathematica, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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