Local Whittle Estimation of Multivariate Fractionally Integrated Processes [PDF]
SSRN Electronic Journal, 2009 Summary: This article derives a semi-parametric estimator of multi-variate fractionally integrated processes covering both stationary and non-stationary values of \(d\). We utilize the notion of the extended discrete Fourier transform and periodogram to extend the multi-variate local Whittle estimator of \textit{K.
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Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions [PDF]
, 2008 It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ \xi_j $ for $ j \in \mathbb Z,
Cohen, Serge, Dombry, Clément
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Level set approach for fractional mean curvature flows [PDF]
, 2009 This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set.
Imbert, Cyril
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Advances in Mathematical Physics, 2022 In this paper, the local fractional version of homotopy perturbation method (HPM) is established for a new class of local fractional integral-differential equation (IDE). With the embedded homotopy parameter monotonously changing from 0 to 1, the special
Bo Xu, Sheng Zhang
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Singular and Fractional Integral Operators on Weighted Local Morrey Spaces
Journal of Fourier Analysis and Applications, 2022 We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calderón-Zygmund operators suitably defined on the functions of the space.
Javier Duoandikoetxea, Marcel Rosenthal
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Mild and classical solutions to a fractional singular second order evolution problem
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Existence and uniqueness of mild and classical solutions are discussed for an abstract second-order evolution problem. The nonlinearity contains a local term and a non-local term.
Nasser-Eddine Tatar
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Local pathwise solutions to stochastic evolution equations driven by fractional Brownian motions with Hurst parameters H ∈ (1/3, 1/2] [PDF]
, 2015 In this article we are concerned with the study of the existence and uniqueness of pathwise mild solutions to evolutions equations driven by a H¨older continuous function with H¨older exponent in (1/3, 1/2).
Garrido Atienza, María José +2 more
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About fractional integrals in the space of locally integrable functions
Journal of Mathematical Analysis and Applications, 1992 The authors show that the largest ``natural'' function space, where the Riemann-Liouville fractional integral operator \[ J^ \alpha f(x)={1\over{\Gamma(\alpha)}} \int_ 0^ x (x-t)^{\alpha-1} f(t)dt \] and differential operator \[ D^ \alpha f(x)={1 \over{\Gamma(1-\alpha)}} {d \over dx} \int_ 0^ x (x-t)^{-\alpha} f(t)dt ...
Martinez, Celso +2 more
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The approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators [PDF]
Sahand Communications in Mathematical Analysis, 2016 In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators.
Hassan Kamil Jassim
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Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives
Journal of Mathematics, 2021 A fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising.
Xiaoran Lin +3 more
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