Elastic Brownian motion with random jumps from the boundary
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914132432781312 |
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| author | Colantoni, Fausto D'Ovidio, Mirko |
| author_facet | Colantoni, Fausto D'Ovidio, Mirko |
| contents | In this paper, we study elastic Brownian motion on a \(C^2\) domain. Instead of being killed at the boundary, the process restarts from a random position inside the domain. We characterize this process through its stochastic differential equation (SDE), its generator, and a description of the paths. We also derive the invariant probability measure and the spectral representation. At the end, we focus on the harmonic functions on the upper half-space to study the trace process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elastic Brownian motion with random jumps from the boundary Colantoni, Fausto D'Ovidio, Mirko Probability Analysis of PDEs 60J65, 60J75, 60J60, 35P05, 35J25 In this paper, we study elastic Brownian motion on a \(C^2\) domain. Instead of being killed at the boundary, the process restarts from a random position inside the domain. We characterize this process through its stochastic differential equation (SDE), its generator, and a description of the paths. We also derive the invariant probability measure and the spectral representation. At the end, we focus on the harmonic functions on the upper half-space to study the trace process. |
| title | Elastic Brownian motion with random jumps from the boundary |
| topic | Probability Analysis of PDEs 60J65, 60J75, 60J60, 35P05, 35J25 |
| url | https://arxiv.org/abs/2511.01455 |