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Hokkaido University Preprint Series in Mathematics >
Stochastic control with fixed marginal distributions
| Title: | Stochastic control with fixed marginal distributions |
| Authors: | Mikami, Toshio Browse this author |
| Keywords: | Monge-Kantorovich Problem | | Stochastic control | | fixed marginal distributions Nelson's Problem,Duality Theorem |
| Issue Date: | 24-Aug-2006 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 800 |
| Start Page: | 1 |
| End Page: | 48 |
| Abstract: | We briefly describe the so-called Monge-Kantorovich Problem (MKP for short) which is often referred to as an optimal mass transportation problem and study the stochastic optimal control problem (SOCP for short) with fixed initial and terminal distributions. In particular, we study the so-called Duality Theorem for the SOCP where continuous semimartingales under consideration have a variable diffusion matrix and then discuss the relation between the MKP and the SOCP. We also study the so-called Nelson's Problem, as the SOCP with fixed marginal distributions at each time, to which we give a new approach from the Duality Theorem. We finally consider a class of deterministic variational problems with fixed marginal distributions which is related to the SOCP by extending a class of measures under consideration. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69608 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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