Explicit local density bounds for Itô-processes with irregular drift
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917802719313920 |
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| author | Krühner, Paul Xu, Shijie |
| author_facet | Krühner, Paul Xu, Shijie |
| contents | We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one dimension we extend our result to the case that the diffusion coefficient is a locally Lipschitz-continuous function of the state. Our approach is based on a comparison to a suitable doubly reflected Brownian motion whose density is known in a series representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02241 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit local density bounds for Itô-processes with irregular drift Krühner, Paul Xu, Shijie Probability 60H10, 49N60 We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one dimension we extend our result to the case that the diffusion coefficient is a locally Lipschitz-continuous function of the state. Our approach is based on a comparison to a suitable doubly reflected Brownian motion whose density is known in a series representation. |
| title | Explicit local density bounds for Itô-processes with irregular drift |
| topic | Probability 60H10, 49N60 |
| url | https://arxiv.org/abs/2308.02241 |