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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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Fractional Brownian motion [PDF]
, 2006 There are natural phenomena in which wide variability is commonly observed, most notably the weather. Any expectations of regularity, or independence of this year’s weather from the past or the future, are not borne out by tradition or folklore. Mandelbrot and Wallis [16.1] saw the essence of traditional knowledge expressed in the Old Testament ...
Oksana Banna +3 more
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Oscillatory Fractional Brownian Motion [PDF]
Acta Applicandae Mathematicae, 2013 The authors ``introduce oscillatory analogues of fractional Brownian motion [(fBm)], subfractional Brownian motion [(sfBm)] and other related long range dependent Gaussian processes.'' According to them, the oscillatory fractional Brownian motion (ofBm) is a centered Gaussian process \(\xi ^{H}\), with parameter \(H\in (1/2,1)\) and covariance function
Bojdecki, T. +2 more
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Fractional Brownian Motions [PDF]
Acta Physica Polonica B, 2020 Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ.
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Journal of Mathematics, 2022 In this paper, we consider the fractional-stochastic Boussinesq-Burger system (FSBBS) generated by the multiplicative Brownian motion. The Jacobi elliptic function techniques are used to create creative elliptic, hyperbolic, and rational fractional ...
Wael W. Mohammed +2 more
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ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS
International Journal for Computational Civil and Structural Engineering, 2022 Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters.
Charles El-Nouty, Darya Filatova
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Frontiers in Physics, 2021 In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion.
Lili Gao, Xichao Sun
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On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes
Mathematics, 2019 We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss−Markov process from Doob representation by replacing ...
Mario Abundo, Enrica Pirozzi
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Cluster Analysis on Locally Asymptotically Self-Similar Processes with Known Number of Clusters
Fractal and Fractional, 2022 We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic examples.
Nan Rao, Qidi Peng, Ran Zhao
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Anomalous diffusion: fractional Brownian motion vs fractional Ito motion
Journal of Physics A: Mathematical and Theoretical, 2022 AbstractGeneralizing 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. As BM, also FBM is a symmetric and Gaussian process, with a continuous trajectory, and with a stationary ...
Iddo Eliazar, Tal Kachman
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