fractional Brownian motion process
Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?
... integral process driven by a fractional Brownian motion is the admission of arbitrage when the integral is defined in a pathwise Stieltjes way, in ...using fractional Brwonian ...
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Long range dependent processes and fractional Brownian motion
... stochastic process m eans certain continuity of th e second m om ents, or the covariance functions of the ...includes Brownian m otion as an exam ...of fractional Brownian ...
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Hurst exponents, Markov processes, and fractional Brownian motion
... First, note that if the increments are nonstationary, then even if we know the Green function g we don’t know the corresponding density for the increments. To prove that a Markov process guarantess uncorrelated ...
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Ergodicity of hypoeliptic SDEs driven by fractional Brownian motion
... On the other hand, our definition of an invariant measure is more restrictive than that of a random invariant measure in [Arn98]. Since it generalises the notion of an invariant measure for a Markov process, this ...
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Synthesis of Mammographic Images Based on the Fractional Brownian Motion
... interesting because of the variety of background tissues and irregular shapes of microcalcifications. As previously mentioned, the fBm can be adequate to simulate ROIs of mammograms [8]. In this section, some basic ...
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Nonlocal fractional stochastic differential equations driven by fractional Brownian motion
... by fractional Brow- nian motion or fractional stochastic differential equations with Wiener ...for fractional stochastic differential equations driven by fBm has not been investigated in the ...
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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 ...multifractional Brownian motion (mfBm), see ...Gaussian process { B α(t) (t), t ≥ ...
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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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Geometric Fractional Brownian Motion Perturbed by Fractional Ornstein Uhlenbeck Process and Application on KLCI Option Pricing
... We presented a new model which is a GFBM providing that the volatility is assumed stochastic that obeys frac- tional Orenstein-Uhlenbeck process. To estimate the parameters involved in this model, we have to ...
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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 ...Gaussian process ...
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Weak convergence of the complex fractional Brownian motion
... two other counter processes where, at each jump of M, each of them jumps or does not jump with probability 1 2 , independently of the jumps of the other process and of its past. In Bardina et al. [4], they proved ...
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A unifying approach to fractional Lévy processes
... to fractional L´ evy ...evy process and the lower bound on the Blumenthal-Getoor index, ...evy process ensures the existence of fractional L´ evy ...to fractional Brownian ...for ...
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Stochastic delay evolution equations driven by sub fractional Brownian motion
... stochastic process with Hölder continuous trajectories of order β > – H, then the path-wise Riemann-Stieltjes integral T u t (ω) dS H (t)(ω) exists for all T ≥ (see Young ...
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Stochastic modified Boussinesq approximate equation driven by fractional Brownian motion
... Ornstein-Uhlenbeck process is introduced. By the stationary property of the fractional Ornstein-Uhlenbeck process, we can use the Birkhoff-Chintchin ergodic theorem to con- vert the integration over ...
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On the non Lipschitz stochastic differential equations driven by fractional Brownian motion
... Markov process, we definitely lost good inequalities such as the Burkholder-Davis-Gundy inequal- ity, which is crucial for SDEs driven by Brownian ...
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Controllability of a stochastic functional differential equation driven by a fractional Brownian motion
... of Brownian motion, fractional Brownian motion (fBm) is a self- similar Gaussian processes which have the properties of long/short-range ...with Brownian motion, the ...
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Controllability of a Stochastic Neutral Functional Differential Equation Driven by a fBm
... of Brownian motion, fractional Brownian motion (fBm) is a self-similar Gaussian process which has the properties of long/short-range ...However, fractional Brownian ...
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Research on Cutting Tool Wear Based on Fractional Brownian Motion
... In the machining process, the tool wear will affect the surface quality and dimensional accuracy of the artifacts. Therefore, monitoring and predicting tool wear more accurately are currently an urgent issue to be ...
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A weighted random walk approximation to fractional Brownian motion
... to fractional Brownian motion in the literature (see, ...the fractional random walk is given as a weighted sum of past increments of an ordinary (Bernoulli) random ...the process and is ...
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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 ...This ...
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