On the minimal integral energy of majorants of the Wiener process
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913958414254080 |
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| author | Nikitin, S. E. |
| author_facet | Nikitin, S. E. |
| contents | We consider the asymptotic behavior (over long time intervals) of the minimal integral energy \[ |h|_T^ψ= \int_0^T ψ(h^\prime(t)) \, \mathrm{d}t \] of majorants of the Wiener process $ W(\cdot) $ satisfying the constraints $ h(0) = r $, $ h(t) \geq W(t) $ for $ 0 \leq t \leq T $. The results significantly generalize previous asymptotic estimates obtained for the case of kinetic energy $ ψ(u) = u^2 $, revealing that this case, where the minimal energy grows logarithmically, is a critical one, lying between two different asymptotic regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the minimal integral energy of majorants of the Wiener process Nikitin, S. E. Probability 60G15, 60G17, 60F15 We consider the asymptotic behavior (over long time intervals) of the minimal integral energy \[ |h|_T^ψ= \int_0^T ψ(h^\prime(t)) \, \mathrm{d}t \] of majorants of the Wiener process $ W(\cdot) $ satisfying the constraints $ h(0) = r $, $ h(t) \geq W(t) $ for $ 0 \leq t \leq T $. The results significantly generalize previous asymptotic estimates obtained for the case of kinetic energy $ ψ(u) = u^2 $, revealing that this case, where the minimal energy grows logarithmically, is a critical one, lying between two different asymptotic regimes. |
| title | On the minimal integral energy of majorants of the Wiener process |
| topic | Probability 60G15, 60G17, 60F15 |
| url | https://arxiv.org/abs/2507.17468 |