Recurrence of the random process governed with the fractional Laplacian and the Caputo time derivative
| Autor: | Affili, Elisa, Kemppainen, Jukka T. |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| DOI: | 10.6092/issn.2240-2829/17264 |
| Popis: | 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. Bruno Pini Mathematical Analysis Seminar, Vol. 14 No. 1 (2023): Nonlocal and Nonlinear PDEs at the University of Bologna |
| Databáze: | OpenAIRE |
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