東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Stochastic optimal transportation = ...

Mikami, Toshio.

Linked to FindBook

Google Book

Amazon

博客來

Stochastic optimal transportation = stochastic control with fixed marginals /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stochastic optimal transportation/ by Toshio Mikami.
Reminder of title:	stochastic control with fixed marginals /
Author:	Mikami, Toshio.
Published:	Singapore :Springer Singapore : : 2021.,
Description:	xi, 121 p. :ill., digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction -- Chapter 2. Stochastic optimal transportation problem -- Chapter 3. Marginal problem.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes. -
Online resource:	https://doi.org/10.1007/978-981-16-1754-6
ISBN:	9789811617546

Stochastic optimal transportation = stochastic control with fixed marginals /
Mikami, Toshio.

Stochastic optimal transportationstochastic control with fixed marginals /[electronic resource] :by Toshio Mikami. - Singapore :Springer Singapore :2021. - xi, 121 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Chapter 1. Introduction -- Chapter 2. Stochastic optimal transportation problem -- Chapter 3. Marginal problem.

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 Schrodinger'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 Schrodinger'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 introduced to 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 problem with a quadratic cost and the duality theorem for the OT are described. Also described are the Lipschitz continuity and the semiconcavity of Schrodinger's problem in marginal distributions and random variables with given marginals, respectively. As well, there is an explanation of the regularity result for the solution to Schrodinger's functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schrodinger's problem can be considered a class of mean field games. The construction of stochastic processes with given marginals, called the marginal problem for stochastic processes, is discussed as an application of the SOT and the OT.

ISBN: 9789811617546

Standard No.: 10.1007/978-981-16-1754-6doiSubjects--Topical Terms:

520663
Stochastic processes.

LC Class. No.: QA274 / .M553 2021

Dewey Class. No.: 519.23

Stochastic optimal transportation = stochastic control with fixed marginals /
LDR:03119nmm a2200349 a 4500 001 2244844
003 DE-He213
005 20210702072724.0
006 m d
007 cr nn 008maaau
008 211207s2021 si s 0 eng d
020 $a 9789811617546 $q (electronic bk.)
020 $a 9789811617539 $q (paper)
024 7 $a 10.1007/978-981-16-1754-6 $2 doi
035 $a 978-981-16-1754-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274 $b .M553 2021
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.23 $2 23
090 $a QA274 $b .M636 2021
100 1 $a Mikami, Toshio. $3 3506131
245 1 0 $a Stochastic optimal transportation $h [electronic resource] : $b stochastic control with fixed marginals / $c by Toshio Mikami.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2021.
300 $a xi, 121 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a Chapter 1. Introduction -- Chapter 2. Stochastic optimal transportation problem -- Chapter 3. Marginal problem.
520 $a 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 Schrodinger'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 Schrodinger'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 introduced to 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 problem with a quadratic cost and the duality theorem for the OT are described. Also described are the Lipschitz continuity and the semiconcavity of Schrodinger's problem in marginal distributions and random variables with given marginals, respectively. As well, there is an explanation of the regularity result for the solution to Schrodinger's functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schrodinger's problem can be considered a class of mean field games. The construction of stochastic processes with given marginals, called the marginal problem for stochastic processes, is discussed as an application of the SOT and the OT.
650 0 $a Stochastic processes. $3 520663
650 0 $a Transportation $x Statistical methods. $3 778962
650 1 4 $a Probability Theory and Stochastic Processes. $3 891080
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Analysis. $3 891106
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Measure and Integration. $3 891263
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u https://doi.org/10.1007/978-981-16-1754-6
950 $a Mathematics and Statistics (SpringerNature-11649)