Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 235-255, 2019


The dyadic fractional diffusion kernel as a central limit

Hugo Aimar, Ivana Gómez, Federico Morana

Received June 2, 2017.   Published online July 26, 2018.

Abstract:  We obtain the fundamental solution kernel of dyadic diffusions in $\mathbb{R}^+$ as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis.
Keywords:  central limit theorem; dyadic diffusion; fractional diffusion; stable process; wavelet analysis
Classification MSC:  60F05, 60G52, 35R11
DOI:  10.21136/CMJ.2018.0274-17


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Affiliations:   Hugo Aimar, Ivana Gómez, Federico Morana, Instituto de Matemática Aplicada del Litoral, UNL, CONICET, Colectora Ruta Nac. No. 168, Paraje El Pozo, 3000 Santa Fe, Argentina, e-mail: haimar@santafe-conicet.gov.ar, ivanagomez@santafe-conicet.gov.ar, fmorana@santafe-conicet.gov.ar


 
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