| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2019-03-08T15:01:18Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147630 |
| . |
| 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 |
| . |
