Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915550099144704 |
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| author | Bonaccorsi, Stefano Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni |
| author_facet | Bonaccorsi, Stefano Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni |
| contents | We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems. Our main focus is on Feller-Wentzell diffusions with jumps (resetting/restart). We first consider the instructive case of the real line, then we extend our results on star graphs with trapping points or repulsive vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14135 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs Bonaccorsi, Stefano Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni Probability Analysis of PDEs We consider dynamic boundary conditions involving non-local operators. Our analysis includes a detailed description of such operators together with their relations with random times and random (additive) functionals. We provide some new characterizations for the boundary behaviour of the Brownian motion based on the interplay between non-local operators and boundary value problems. Our main focus is on Feller-Wentzell diffusions with jumps (resetting/restart). We first consider the instructive case of the real line, then we extend our results on star graphs with trapping points or repulsive vertices. |
| title | Non-local Boundary Value Problems, stochastic resetting and Brownian motions on graphs |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2209.14135 |