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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2403.17305 |
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| _version_ | 1866913283461611520 |
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| author | Herry, Ronan Huguet, Baptiste |
| author_facet | Herry, Ronan Huguet, Baptiste |
| contents | Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, Léonard & Zambrini (AIHP PS 2020), we study a problem of entropic minimization on the path space when the reference measure is a generic Feller semimartingale. We show that, under some regularity condition, our problem connects naturally with a, possibly non-local, version of the Hamilton-Jacobi-Bellman equation. Additionally, we study existence of minimizers when the reference measure in a Ornstein-Uhlenbeck process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Brenier-Schrödinger problem with respect to Feller semimartingales and non-local Hamilton-Jacobi-Bellman equations Herry, Ronan Huguet, Baptiste Probability Analysis of PDEs 60G53 (Primary), 49Q20 (Secondary) Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, Léonard & Zambrini (AIHP PS 2020), we study a problem of entropic minimization on the path space when the reference measure is a generic Feller semimartingale. We show that, under some regularity condition, our problem connects naturally with a, possibly non-local, version of the Hamilton-Jacobi-Bellman equation. Additionally, we study existence of minimizers when the reference measure in a Ornstein-Uhlenbeck process. |
| title | The Brenier-Schrödinger problem with respect to Feller semimartingales and non-local Hamilton-Jacobi-Bellman equations |
| topic | Probability Analysis of PDEs 60G53 (Primary), 49Q20 (Secondary) |
| url | https://arxiv.org/abs/2403.17305 |