Time reversal of reflected Brownian motion with Poissonian resetting
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911167286345728 |
|---|---|
| author | Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni |
| author_facet | Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni |
| contents | In this paper, we study reflecting Brownian motion with Poissonian resetting. After providing a probabilistic description of the phenomenon using jump diffusions and semigroups, we analyze the time-reversed process starting from the stationary measure. We prove that the time-reversed process is a Brownian motion with a negative drift and non-local boundary conditions at zero. Moreover, we further study the time-reversed process between two consecutive resetting points and show that, within this time window, it behaves as the same reflecting Brownian motion with a negative drift, where both the jump sizes and the time spent at zero coincide with those of the process obtained under the stationary measure. We characterize the dynamics of both processes, their local times, and finally investigate elliptic problems on positive half-spaces, showing that the two processes leave the same traces at the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time reversal of reflected Brownian motion with Poissonian resetting Colantoni, Fausto D'Ovidio, Mirko Pagnini, Gianni Probability In this paper, we study reflecting Brownian motion with Poissonian resetting. After providing a probabilistic description of the phenomenon using jump diffusions and semigroups, we analyze the time-reversed process starting from the stationary measure. We prove that the time-reversed process is a Brownian motion with a negative drift and non-local boundary conditions at zero. Moreover, we further study the time-reversed process between two consecutive resetting points and show that, within this time window, it behaves as the same reflecting Brownian motion with a negative drift, where both the jump sizes and the time spent at zero coincide with those of the process obtained under the stationary measure. We characterize the dynamics of both processes, their local times, and finally investigate elliptic problems on positive half-spaces, showing that the two processes leave the same traces at the boundary. |
| title | Time reversal of reflected Brownian motion with Poissonian resetting |
| topic | Probability |
| url | https://arxiv.org/abs/2505.15639 |