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Recurrence of the random process governed with the fractional Laplacian and the Caputo time derivative |
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| Author: | Affili, Elisa1; Kemppainen, Jukka T.2 |
| Organizations: |
1Università di Bologna, Dipartimento di Matematica 2University of Oulu, Applied and Computational Mathematics, Faculty of Information Technology and Electrical Engineering |
| Format: | article |
| Version: | published version |
| Access: | open |
| Online Access: | PDF Full Text (PDF, 0.3 MB) |
| Persistent link: | http://urn.fi/urn:nbn:fi-fe20231018140536 |
| Language: | English |
| Published: |
Università di Bologna,
2023
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| Publish Date: | 2023-10-18 |
| Description: |
AbstractWe 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. see all
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| Series: |
Bruno Pini mathematical analysis seminar |
| ISSN: | 2240-2829 |
| ISSN-E: | 2240-2829 |
| ISSN-L: | 2240-2829 |
| Volume: | 14 |
| Issue: | 1 |
| Pages: | 1 - 14 |
| DOI: | 10.6092/issn.2240-2829/17264 |
| OADOI: | https://oadoi.org/10.6092/issn.2240-2829/17264 |
| Type of Publication: |
A1 Journal article – refereed |
| Field of Science: |
111 Mathematics |
| Subjects: | |
| Copyright information: |
© 2023 Elisa Affili, Jukka T. Kemppainen. This work is licensed under a Creative Commons Attribution 3.0 Unported License. |
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https://creativecommons.org/licenses/by/3.0/ |