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重分数布朗运动的列维连续模(Lévy's moduli of continuity of multifractional Brownian motion)
Zhejiang Daxue xuebao. Lixue ban, 2000 This paper proposed Lévy's moduli of continuity of multifractional Brownian motion,which is a generalization of the fractional Brownian motion.
LINZheng-yan(林正炎)
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Mixed Fractional Brownian Motion [PDF]
Bernoulli, 2001 We show that the sum of a Brownian motion and a non-trivial multiple of an independent fractional Brownian motion with Hurst parameter H ∈ (0,1] is not a semimartingale if H ∈ (0, ½) ∪ (½, ¾], that it is equivalent to a multiple of Brownian motion if H = ½ and equivalent to Brownian motion if H ∈ ( ¾ , 1].
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Extremes of spherical fractional Brownian motion [PDF]
Extremes, 2019 Let $\{B_ (x), x \in \mathbb{S}^N\}$ be a fractional Brownian motion on the $N$-dimensional unit sphere $\mathbb{S}^N$ with Hurst index $ $. We study the excursion probability $\mathbb{P}\{\sup_{x\in T} B_ (x) > u \}$ and obtain the asymptotics as $u\to \infty$, where $T$ can be the entire sphere $\mathbb{S}^N$ or a geodesic disc on $\mathbb{S}^N$
Cheng, Dan, Liu, Peng
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Fractional Brownian motion [PDF]
, 2006 Fractional Brownian motion is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium-or long-memory property which is in sharp contrast with martingales and Markov
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Are Fractional Brownian Motions Predictable? [PDF]
, 2011 We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor.
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Fractional Brownian motion in a nutshell [PDF]
International Journal of Modern Physics: Conference Series, 2015 This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of the 7th Jagna International Workshop.
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A Set-indexed Fractional Brownian Motion [PDF]
Journal of Theoretical Probability, 2006 We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is relaxed. Relations with the Levy fractional Brownian motion and with the fractional Brownian sheet are studied.
Erick Herbin, Ely Merzbach
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Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries [PDF]
New Journal of Physics, 2019 Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes.
T. Guggenberger +4 more
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Fractal and FractionalTempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of the second kind (TFBMII) modify the power-law kernel in the moving average representation of fractional Brownian motion by introducing exponential tempering.
Yuliya Mishura, Kostiantyn Ralchenko
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Fractional Brownian Motion and the Markov Property
Electronic Communications in Probability, 1998 9 ...
Coutin, Laure, Carmona, Philippe
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