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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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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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A DYNAMICAL APPROACH TO FRACTIONAL BROWNIAN MOTION [PDF]
Fractals, 1994 Herein we develop a dynamical foundation for fractional Brownian motion. A clear relation is established between the asymptotic behavior of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is applicable, we establish a connection between diffusion (either standard or anomalous) and the dynamical indicator known
MANNELLA, RICCARDO +2 more
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Generating Diffusions with Fractional Brownian Motion
Communications in Mathematical Physics, 2022 AbstractWe study fast/slow systems driven by a fractional Brownian motion B with Hurst parameter $$H\in (\frac{1}{3}, 1]$$ H ∈ ( 1 3 , 1
Martin Hairer, Xue-Mei Li
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Option Pricing under the Subordinated Market Models
Discrete Dynamics in Nature and Society, 2022 This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity ...
Longjin Lv, Changjuan Zheng, Luna Wang
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Crossover dynamics of climate change models: Numerical simulations
Alexandria Engineering Journal, 2023 In this paper, two new climate change mathematical models are extended using the stochastic-deterministic piecewise hybrid fractional derivatives, where the hybrid fractional order operator is applied to extend the deterministic model and the fractional ...
N.H. Sweilam +4 more
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Fractional Brownian fields, duality, and martingales
, 2006 In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations of fractional
Dobrić, Vladimir, Ojeda, Francisco M.
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A fractional Brownian field indexed by $L^2$ and a varying Hurst parameter [PDF]
, 2014 Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional ...
Richard, Alexandre
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Approximation of Fractional Brownian Motion by Martingales [PDF]
Methodology and Computing in Applied Probability, 2012 We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.
Shklyar, Sergiy +4 more
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Central limit theorem for an additive functional of the fractional Brownian motion II [PDF]
, 2013 We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{2+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in ...
Nualart, David, Xu, Fangjun
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