Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914789603672064 |
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| author | Aurzada, Frank Kolb, Martin Schickentanz, Dominic T. |
| author_facet | Aurzada, Frank Kolb, Martin Schickentanz, Dominic T. |
| contents | We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behaviour of the probability that a Brownian motion on $[0,T]$ spends limited time outside a bounded interval, as $T \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04866 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion Aurzada, Frank Kolb, Martin Schickentanz, Dominic T. Probability 60J65, 60J55 We show that a Brownian motion on $\mathbb{R}_{\ge 0}$ which is allowed to spend a total of $s > 0$ time units outside a bounded interval does not leave the interval at all. This can be seen as an extreme example of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behaviour of the probability that a Brownian motion on $[0,T]$ spends limited time outside a bounded interval, as $T \to \infty$. |
| title | Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion |
| topic | Probability 60J65, 60J55 |
| url | https://arxiv.org/abs/2308.04866 |