Sample path properties of fractional Riesz–Bessel field of variable order

In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable random fields (TRF, for short). TRF is typically non-Gaussian and generalizes tempered fractional stable stochastic processes. TRF comprises moving average and harmonizable-type subclasses that are constructed by tempering (matrix-) homogeneous, matrix-valued kernels in time-and Fourier-domain stochastic integrals with respect to vector-valued, strictly operator-stable random measures. We establish the existence and fundamental properties of TRF. Assuming both Gaussianity and isotropy, we show the equivalence between certain moving average and harmonizable subclasses of TRF. In addition, we establish sample path properties in the scalar-valued case for several Gaussian instances.

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“…where we make the change of variable λy = y ′ and apply the formula Lim and Teo (2008), p. 013509-3). Note that the matrix-valued function…”

Section: Appendix B Section 4: Proofsmentioning

confidence: 99%

On multivariate fractional random fields: tempering and operator-stable laws

Didier

Kanamori

Sabzikar

2020

Preprint

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“…where θ = (θ 1 , θ 2 , θ 3 ) = (α, β, γ) ∈ Θ = (α, α) × (β, β) × (γ, γ), α > 0, α < 1 2 , β > 0, β < ∞, γ > 1 2 , γ < ∞, and the parameter α signifies the long range dependence, while the parameter γ indicates the second-order intermittency [4,16,46], the weight functions have been chosen in the form…”

Section: Example the Motion Of A Pendulum In A Turbulent Fluidmentioning

confidence: 99%

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Ivanov

Leonenko

Orlovskyi

2019

Stat Inference Stoch Process

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A continuous-time nonlinear regression model with LГқvy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper. IntroductionThe paper is focused on such an important aspect of the study of regression models with correlated observations as an estimation of random noise functional characteristics. When considering this problem the regression function unknown parameter becomes nuisance and complicates the analysis of noise. To neutralise its presence, we must estimate the parameter and then build estimators, say, of spectral density parameter of a stationary random noise using residuals, that is the difference between the values of the observed process and fitted regression function.So, in the first step we employ the least squares estimator (LSE) for unknown parameter of nonlinear regression, because of its relative simplicity. Asymptotic properties of the LSE in nonlinear regression model were studied by many authors. Numerous results on the subject can be found in monograph by Ivanov and Leonenko [34], Ivanov [32].

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“…It has been known as a great way in the field of modeling real problems in many fields [20][21][22]. Some procedures are elaborated to find exact or numerical solution to such complex derivative [23,24]. More references on VO fractional models are cited, for VO fractional diffusion model [25], difference between VO and constant order models [26].…”

Section: Introductionmentioning

confidence: 99%

Pulsatile blood flow in constricted tapered artery using a variable-order fractional Oldroyd-B model

2017

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The aim of this paper is to deal with the pulsatile flow of blood in stenosed arteries using one of the known constitutive models that describe the viscoelasticity of blood witch is the generalized Oldroyd-B model with a variable-order fractional derivative. Numerical approximation for the axial velocity and wall shear stress were obtained by use of the implicit finite-difference scheme. The velocity profile is analyzed by graphical illustrations. This mathematical model gives more realistic results that will help medical practitioners and it has direct applications in the treatment of cardiovascular diseases.

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Sample path properties of fractional Riesz–Bessel field of variable order

Cited by 11 publications

References 57 publications

On multivariate fractional random fields: tempering and operator-stable laws

On multivariate fractional random fields: tempering and operator-stable laws

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Pulsatile blood flow in constricted tapered artery using a variable-order fractional Oldroyd-B model

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