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Recurrence of the random process governed with the fractional Laplacian and the Caputo time derivative
- Source :
- Bruno Pini Mathematical Analysis Seminar, Vol 14, Iss 1, Pp 1-14 (2023)
- Publication Year :
- 2023
- Publisher :
- University of Bologna, 2023.
-
Abstract
- We are addressing a parabolic equation with fractional derivatives in time and space that governs the scaling limit of continuous-time random walks with anomalous diffusion. For these equations, the fundamental solution represents the probability density of finding a particle released at the origin at time 0 at a given position and time. Using some estimates of the asymptotic behaviour of the fundamental solution, we evaluate the probability of the process returning infinite times to the origin in a heuristic way. Our calculations suggest that the process is always recurrent.
Details
- Language :
- English, Italian
- ISSN :
- 22402829
- Volume :
- 14
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Bruno Pini Mathematical Analysis Seminar
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.46ef5afd51d74c10b04331433c22e601
- Document Type :
- article
- Full Text :
- https://doi.org/10.6092/issn.2240-2829/17264