An excursion onto Schrödinger's bridges: Stochastic flows with spatio-temporal marginals
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917699980886016 |
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| author | Eldesoukey, Asmaa Miangolarra, Olga Movilla Georgiou, Tryphon T. |
| author_facet | Eldesoukey, Asmaa Miangolarra, Olga Movilla Georgiou, Tryphon T. |
| contents | The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schrödinger bridges, by incorporating termination (killing) of stochastic flows. Specifically, in the context of estimation, we seek the most likely evolution realizing measured spatio-temporal marginals of killed particles. In the context of control, we seek a suitable control action directing the killed process toward spatio-temporal probabilistic constraints. To this end, we derive a new Schrödinger system of coupled, in space and time, partial differential equations to construct the solution of the proposed problem. Further, we show that a Fortet-Sinkhorn type of algorithm is available to attain the associated bridge. A key feature of our framework is that the obtained bridge retains the Markovian structure in the prior process, and thereby, the corresponding controller takes the form of state feedback. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An excursion onto Schrödinger's bridges: Stochastic flows with spatio-temporal marginals Eldesoukey, Asmaa Miangolarra, Olga Movilla Georgiou, Tryphon T. Optimization and Control Systems and Control Probability 60J10, 92Exx, 62B10 The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schrödinger bridges, by incorporating termination (killing) of stochastic flows. Specifically, in the context of estimation, we seek the most likely evolution realizing measured spatio-temporal marginals of killed particles. In the context of control, we seek a suitable control action directing the killed process toward spatio-temporal probabilistic constraints. To this end, we derive a new Schrödinger system of coupled, in space and time, partial differential equations to construct the solution of the proposed problem. Further, we show that a Fortet-Sinkhorn type of algorithm is available to attain the associated bridge. A key feature of our framework is that the obtained bridge retains the Markovian structure in the prior process, and thereby, the corresponding controller takes the form of state feedback. |
| title | An excursion onto Schrödinger's bridges: Stochastic flows with spatio-temporal marginals |
| topic | Optimization and Control Systems and Control Probability 60J10, 92Exx, 62B10 |
| url | https://arxiv.org/abs/2404.07402 |