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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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Statistical analysis of superstatistical fractional Brownian motion and applications.
Physical Review E, 2019Recent advances in experimental techniques for complex systems and the corresponding theoretical findings show that in many cases random parametrization of the diffusion coefficients gives adequate descriptions of the observed fractional dynamics.
Arleta Maćkała, M. Magdziarz
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Trading Fractional Brownian Motion
SIAM Journal on Financial Mathematics, 2019In 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...
P. Guasoni, Zsolt Nika, M. Rásonyi
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Stochastic Analysis and Applications, 2019
This paper concerns a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter . The existence and uniqueness of almost automorphic solutions in distribution of mean field stochastic differential ...
Fengxi Chen, Xiaoying Zhang
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This paper concerns a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter . The existence and uniqueness of almost automorphic solutions in distribution of mean field stochastic differential ...
Fengxi Chen, Xiaoying Zhang
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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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Pricing of perpetual American put option with sub-mixed fractional Brownian motion
Fractional Calculus and Applied Analysis, 2019The pricing problem of perpetual American put options is investigated when the underlying asset price follows a sub-mixed fractional Brownian motion process.
Feng Xu, Shengwu Zhou
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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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