Left-inverses of fractional Laplacian and sparse stochastic processes

DOI10.1007/s10444-011-9183-6zbMath1251.26006arXiv1009.2651OpenAlexW2148407475MaRDI QIDQ453546

Qiyu Sun, Michael Unser

Publication date: 27 September 2012

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2651

zbMATH Keywords

Riesz potentialfractional Laplacianfractional stochastic processimpulsive Poisson noisestochastic partial differential operator

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Fractional derivatives and integrals (26A33) PDEs with randomness, stochastic partial differential equations (35R60) Functional-differential equations with fractional derivatives (34K37)

Related Items (7)

Models of space-fractional diffusion: a critical review ⋮ Waveform relaxation method for fractional differential-algebraic equations ⋮ A stochastic fractional Laplace equation driven by colored noise on bounded domain, and its covariance functional ⋮ On the continuity of characteristic functionals and sparse stochastic modeling ⋮ Wavelet Statistics of Sparse and Self-Similar Images ⋮ Scaling limits of solutions of linear stochastic differential equations driven by Lévy white noises ⋮ Waveform relaxation methods for fractional functional differential equations

Cites Work

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• Self-Similarity: Part II—Optimal Estimation of Fractal Processes
• Stochastic Models for Sparse and Piecewise-Smooth Signals
• Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes
• Holder estimates for solutions of integro differential equations like the fractional laplace
• Fractional Brownian Motions, Fractional Noises and Applications

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