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Title: The dyadic fractional diffusion kernel as a central limit (English)
Author: Aimar, Hugo
Author: Gómez, Ivana
Author: Morana, Federico
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 69
Issue: 1
Year: 2019
Pages: 235-255
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: central limit theorem
Keyword: dyadic diffusion
Keyword: fractional diffusion
Keyword: stable process
Keyword: wavelet analysis
MSC: 35R11
MSC: 60F05
MSC: 60G52
idZBL: Zbl 07088782
idMR: MR3923587
DOI: 10.21136/CMJ.2018.0274-17
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Date available: 2019-03-08T15:01:18Z
Last updated: 2019-09-26
Stable URL: http://hdl.handle.net/10338.dmlcz/147630
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Reference: [1] Actis, M., Aimar, H.: Dyadic nonlocal diffusions in metric measure spaces.Fract. Calc. Appl. Anal. 18 (2015), 762-788. Zbl 1320.43003, MR 3351499, 10.1515/fca-2015-0046
Reference: [2] Actis, M., Aimar, H.: Pointwise convergence to the initial data for nonlocal dyadic diffusions.Czech. Math. J. 66 (2016), 193-204. Zbl 06587883, MR 3483232, 10.1007/s10587-016-0249-y
Reference: [3] Aimar, H., Bongioanni, B., Gómez, I.: On dyadic nonlocal Schrödinger equations with Besov initial data.J. Math. Anal. Appl. 407 (2013), 23-34. Zbl 1306.35106, MR 3063102, 10.1016/j.jmaa.2013.05.001
Reference: [4] Bucur, C., Valdinoci, E.: Nonlocal Diffusion and Applications.Lecture Notes of the Unione Matematica Italiana 20, Springer, Cham (2016). Zbl 06559661, MR 3469920, 10.1007/978-3-319-28739-3
Reference: [5] Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian.Commun. Partial Differ. Equations 32 (2007), 1245-1260. Zbl 1143.26002, MR 2354493, 10.1080/03605300600987306
Reference: [6] Chung, K. L.: A Course in Probability Theory.Academic Press, San Diego (2001). Zbl 0980.60001, MR 1796326
Reference: [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). Zbl 06684812, MR 3617721, 10.1007/978-88-7642-601-8
Reference: [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. Zbl 1242.60047, MR 2584076
Reference: [9] Wojtaszczyk, P.: A Mathematical Introduction to Wavelets.London Mathematical Society Student Texts 37, Cambridge University Press, Cambridge (1997). Zbl 0865.42026, MR 1436437, 10.1017/CBO9780511623790
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