Results 1 to 10 of about 243,967 (218)
Reflected fractional Brownian motion in one and higher dimensions. [PDF]
Phys Rev E, 2020 Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion.
Vojta T +5 more
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Fractal and Fractional, 2022 As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention.
Hongwen Hu +3 more
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Generalized fractional Brownian motion [PDF]
Modern Stochastics: Theory and Applications, 2017 We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena.
Mounir Zili
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Impulsive stochastic fractional differential equations driven by fractional Brownian motion
Advances in Difference Equations, 2020 In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional Brownian motion with Hurst index 1 ...
Mahmoud Abouagwa, Feifei Cheng, Ji Li
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Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions. [PDF]
Chaos, 2022 Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems.
Michał Balcerek +4 more
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Distribution dependent SDEs driven by additive fractional Brownian motion [PDF]
Probability theory and related fields, 2021 We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $$H\in (0,1)$$ H ∈ ( 0 , 1 ) . We establish strong well-posedness under a
Lucio Galeati +2 more
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Forecasting with fractional Brownian motion: a financial perspective [PDF]
Quantitative finance (Print), 2021 The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian ...
Matthieu Garcin
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Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions [PDF]
Journal of Physics A: Mathematical and Theoretical, 2021 We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise (FGN) in a superharmonic external potential of the form U(x) ∝ x 2n ( n∈N ).
T. Guggenberger, A. Chechkin, R. Metzler
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Bayesian inference of scaled versus fractional Brownian motion [PDF]
Journal of Physics A: Mathematical and Theoretical, 2021 We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion.
S. Thapa +5 more
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Anomalous diffusion: fractional Brownian motion vs fractional Ito motion [PDF]
Journal of Physics A: Mathematical and Theoretical, 2021 Generalizing Brownian motion (BM), fractional Brownian motion (FBM) is a paradigmatic selfsimilar model for anomalous diffusion. Specifically, varying its Hurst exponent, FBM spans: sub-diffusion, regular diffusion, and super-diffusion.
I. Eliazar, Tal Kachman
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