Fractional Brownian Motion Models
Synthesis of Mammographic Images Based on the Fractional Brownian Motion
... In this work, the fBm was investigated to synthesize ROIs of mammographic images. Four groups of synthetic images were generated: healthy group and with microcalcifications group for the both type of tissue (fatty and ...
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Ruin problems of a two-dimensional fractional Brownian motion risk process
... such models is of particular ...risk models are often approximated by the Bm (also called diffusion) ...risk models have been the subject of study of numerous contributions; see, ...
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Extremes of a(t)-locally stationary Gaussian random fields
... the fractional Brownian motion (fBm) appears in the definition of the Pickands constant, see ...theoretical models and ...multifractional Brownian motion (mfBm), see ...
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Strong Local Non Determinism of Sub Fractional Brownian Motion
... The fractional Brownian motion (fBm for short) is the best known and most used process with long-dependence property for models in telecommunications, turbulence, image processing and ...
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Long range dependent processes and fractional Brownian motion
... ple, models w ith weak dependence (such as ARMA models and Markov processes) are well known and often used in ...these models, interval estim ates and prediction intervals can differ considerably ...
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The quadratic variation for mixed fractional Brownian motion
... tional Brownian motion (in short, fBm) due to its simple properties and some applications in various scientific areas such as telecommunications, turbulence, image processing, and ...
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Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps
... control. Fractional Brownian motion (fBm) is for a family of Gaussian processes that is indexed by the Hurst parameter H ∈ (0, 1) (see ...standard Brownian motion, in particular it is ...
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Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion
... by Brownian motion and also refer to [1, 2, 4, 5, 11] for those only driven by fractional Brownian motion ...by Brownian motion; Boufoussi and Hajji [2] discussed the ...
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Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
... Figure 2. Dispersion curves for the 3-year turbulence trajectories and the three different stochastic models discussed in Sect. 2.5. Panel (a) shows 512 “eddy-free” trajectories, chosen from a larger set of 1024 ...
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Pricing Study on Two Kinds of Power Options in Jump Diffusion Models with Fractional Brownian Motion and Stochastic Rate
... Geometric Brownian Motion (GBM) assumption for the underlying asset’s price dynamics in the BS model fails to reflect the real facts: market return data display excess kurtosis (peaked and fat-tailed ...
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Fractional chemotaxis diffusion equations
... as fractional Brownian motion (fBm) [19–21] or Continuous Time Random Walks (CTRWs) [22, 23] with long-tailed waiting-time den- sities ...these models are non-Markovian and both exhibit the ...
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Parameter estimation for nonergodic Ornstein Uhlenbeck process driven by the weighted fractional Brownian motion
... The fractional Brownian motion (fBm for short) has already been widely applied in hydrol- ogy, traffic volume prediction, estimation of Hurst exponent of seismic signal, finance, and various other areas ...
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Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?
... of models based on (conditional) un- correlated increments to describe certain financial data sets has been observed since [8] and ...replace Brownian motion with fractional Brownian ...
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Hurst exponents, Markov processes, and fractional Brownian motion
... Finally, (49) yields the range of fat tail exponents 2< µ <∞. For µ>3 the variance is finte and scales with hurst exponent H [6], whereas for 2< µ <3 we obtain the Levy range of exponents and infinite ...
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On the non Lipschitz stochastic differential equations driven by fractional Brownian motion
... On most occasions, the coefficients of SDEs driven by fBm are assumed to satisfy the Lipschitz condition. The existence and uniqueness of solutions of SDEs driven by fBm with Lipschitz condition have been studied by many ...
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Beyond multifractional Brownian motion: new stochastic models for geophysical modelling
... The aim of this work is to present some stochastic pro- cesses obtained as generalizations of mBm which display either of the properties mentioned above, and could be of potential use in geophysics. The remainder of this ...
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Stochastic delay evolution equations driven by sub fractional Brownian motion
... ther a semimartingale nor a Markov process when H = . The fBm is a suitable generaliza- tion of the standard Brownian motion, but exhibits long-range dependence, self-similarity and which has stationary ...
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Fluctuation Analysis to Sequence of Ore-forming Element Based on Fractal-Jump Model
... The fractional Brownian motion model is one of the effective models to describe the ...of fractional Brownian motion and Poisson jump model to establish a jump fractal ...
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Geometric Fractional Brownian Motion Perturbed by Fractional Ornstein Uhlenbeck Process and Application on KLCI Option Pricing
... Stochastic volatility (SV) can be referred to the volatility and common dependence between variables that are permitted to fluctuate over time, instead of remain constant. The main idea in stochastic volatility is that ...
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Evaluation of Geometric Asian Power Options under Fractional Brownian Motion
... In 2005, Y. Wang et al. [18] derived an explicit formula of European power options. And Y. Xiao et al. [19] studied some properties of power options under Brownian motion framework. D. In 2006, Y. Wang et ...
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