| 书目名称 | Stochastic Optimal Transportation | | 副标题 | Stochastic Control w | | 编辑 | Toshio Mikami | | 视频video | | | 概述 | Shows the SOT problem to be partly the generalization of the OT problem and partly Schrödinger‘s problem.Explains fundamental results of the stochastic optimal transportation problem, including dualit | | 丛书名称 | SpringerBriefs in Mathematics | | 图书封面 |  | | 描述 | In this book, the optimal transportation problem (OT) is described as a variational problem for absolutely continuous stochastic processes with fixed initial and terminal distributions. Also described is Schrödinger’s problem, which is originally a variational problem for one-step random walks with fixed initial and terminal distributions. The stochastic optimal transportation problem (SOT) is then introduced as a generalization of the OT, i.e., as a variational problem for semimartingales with fixed initial and terminal distributions. An interpretation of the SOT is also stated as a generalization of Schrödinger’s problem. After the brief introduction above, the fundamental results on the SOT are described: duality theorem, a sufficient condition for the problem to be finite, forward–backward stochastic differential equations (SDE) for the minimizer, and so on. The recent development of the superposition principle plays a crucial role in the SOT. A systematic method is introducedto consider two problems: one with fixed initial and terminal distributions and one with fixed marginal distributions for all times. By the zero-noise limit of the SOT, the probabilistic proofs to Monge’s | | 出版日期 | Book 2021 | | 关键词 | Optimal transportation problem; Schrödinger’s problem; Stochastic optimal transportation problem; Margi | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-16-1754-6 | | isbn_softcover | 978-981-16-1753-9 | | isbn_ebook | 978-981-16-1754-6Series ISSN 2191-8198 Series E-ISSN 2191-8201 | | issn_series | 2191-8198 | | copyright | The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 |
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发表于 2025-3-21 16:32:21
