Geodesic
The dyadic fractional diffusion kernel as a central limit
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 235-255
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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.
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.
DOI : 10.21136/CMJ.2018.0274-17
Classification : 35R11, 60F05, 60G52
Keywords: central limit theorem; dyadic diffusion; fractional diffusion; stable process; wavelet analysis 
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Aimar, Hugo; Gómez, Ivana; Morana, Federico. The dyadic fractional diffusion kernel as a central limit. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 235-255. doi: 10.21136/CMJ.2018.0274-17

[1] Actis, M., Aimar, H.: Dyadic nonlocal diffusions in metric measure spaces. Fract. Calc. Appl. Anal. 18 (2015), 762-788. | DOI | MR | JFM

[2] Actis, M., Aimar, H.: Pointwise convergence to the initial data for nonlocal dyadic diffusions. Czech. Math. J. 66 (2016), 193-204. | DOI | MR | JFM

[3] Aimar, H., Bongioanni, B., Gómez, I.: On dyadic nonlocal Schrödinger equations with Besov initial data. J. Math. Anal. Appl. 407 (2013), 23-34. | DOI | MR | JFM

[4] Bucur, C., Valdinoci, E.: Nonlocal Diffusion and Applications. Lecture Notes of the Unione Matematica Italiana 20, Springer, Cham (2016). | DOI | MR | JFM

[5] Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equations 32 (2007), 1245-1260. | DOI | MR | JFM

[6] Chung, K. L.: A Course in Probability Theory. Academic Press, San Diego (2001). | MR | JFM

[7] Dipierro, S., Medina, M., Valdinoci, E.: Fractional Elliptic Problems with Critical Growth in the Whole of $\mathbb R^n$. Appunti. Scuola Normale Superiore di Pisa (Nuova Series) 15, Edizioni della Normale, Pisa (2017). | DOI | MR | JFM

[8] Valdinoci, E.: From the long jump random walk to the fractional Laplacian. Bol. Soc. Esp. Mat. Apl., S$\vec{ {e}}$MA 49 (2009), 33-44. | MR | JFM

[9] Wojtaszczyk, P.: A Mathematical Introduction to Wavelets. London Mathematical Society Student Texts 37, Cambridge University Press, Cambridge (1997). | DOI | MR | JFM

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