Left-Inverses of Fractional Laplacian and Sparse Stochastic Processes

2010/09/14 by Qiyu Sun, Michaël Unser, Sun, Qiyu +1
Physics and Astronomy · Economics, Econometrics and Finance · #Statistical Mechanics and Entropy #Stochastic processes and financial applications #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1009.2651

Abstract

The fractional Laplacian (-\triangle)^γ/2 commutes with the primary coordination transformations in the Euclidean space \RR^d: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

Related

• The fractional Laplacian with reflections
• Lévy processes linked to the lower-incomplete gamma function
• Indicator fractional stable motions
• Fractional Gamma process and fractional Gamma-subordinated processes
• Geometric Stable processes and related fractional differential equations