Neuware -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 Schr�dinger�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 Schr�dinger�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 problem with a quadratic cost and the duality theorem for the OT are described. Also described are the Lipschitz continuity and the semiconcavity of Schr�dinger�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 Schr�dinger�s functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schr�dinger�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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 136 pp. Englisch.

N� de ref. del art�culo 9789811617539

Contactar al vendedor

Denunciar este art�culo

Detalles bibliogr�ficos

T�tulo: Stochastic Optimal Transportation
Editor: Springer Nature Singapore, Springer Nature Singapore Jun 2021
Fecha de publicaci�n: 2021
Idioma: Ingl�s
ISBN 10: 9811617538
ISBN 13: 9789811617539
Encuadernaci�n: Taschenbuch
Estado: Neu
Dimensiones: 235�mil�metros de ancho por 155 de alto por 8 de largo
Peso: 219 gramos

Acerca de

Sinopsis

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 Schr�dinger'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 Schr�dinger'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 Schr�dinger'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 Schr�dinger's functional equation when the space of Borel probability measures is endowed with a strong or a weak topology, and it is shown that Schr�dinger'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.

Acerca del autor

Charlotte y Peter Fiell son dos autoridades en historia, teor�a y cr�tica del dise�o y han escrito m�s de sesenta libros sobre la materia, muchos de los cuales se han convertido en �xitos de ventas. Tambi�n han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Dise�o del siglo XX, El dise�o industrial de la A a la Z, Scandinavian Design y Dise�o del siglo XXI.

"Sobre este t�tulo" puede pertenecer a otra edici�n de este libro.

Descripci�n de la librer�a

Impressum Thorsten Retsch Buchversand Mimpf2000 Ober�lschnitz 16 95517 Emtmannsberg Deutschland Telefon: 09209-2023188 Email: mimpf2000@online.de USt-ID-Nr.: DE 235096871 Wir f�hren gebrauchte B�cher aus allen Sparten der Literatur

Ver la p�gina web de la librer�a

Informaci�n empresarial del vendedor

buchversandmimpf2000
Germany

Condiciones de venta y env�o

Condiciones de venta

Widerrufsbelehrung/ Muster-Widerrufsformular/
Allgemeine Gesch�ftsbedingungen und Kundeninformationen/ Datenschutzerkl�rung

Widerrufsrecht f�r Verbraucher
(Verbraucher ist jede nat�rliche Person, die ein Rechtsgesch�ft zu Zwecken abschlie�t, die �berwiegend weder ihrer gewerblichen noch ihrer selbstst�ndigen beruflichen T�tigkeit zugerechnet werden k�nnen.)

Widerrufsbelehrung

Widerrufsrecht
Sie haben das Recht, binnen 14 Tagen ohne Angabe von Gr�nden diesen Vertrag zu widerrufen.
Die Widerrufsfr...

M�s informaci�n

Derecho a cancelaci�n

Condiciones de env�o

Soweit in der Artikelbeschreibung keine andere Frist angegeben ist, erfolgt die Lieferung der Ware innerhalb von 3-5 Werktagen nach Vertragsschluss, bei Vorauszahlung erst nach Eingang des vollst�ndigen Kaufpreises und der Versandkosten. Alle Preise inkl. MwSt.

Tarifas de env�o de Alemania a Estados Unidos de America

Tarifas de env�o de Alemania a Estados Unidos de America
Cantidad del pedido	De 60 a 60 d�as h�biles	De 60 a 60 d�as h�biles
Primer art�culo	EUR 60.00	EUR 75.00

Los plazos de entrega los establecen los vendedores y var�an seg�n el transportista y la ubicaci�n. Los pedidos que pasan por la aduana pueden sufrir retrasos y los compradores son responsables de los aranceles o tarifas asociadas. Los vendedores pueden ponerse en contacto con usted en relaci�n con cargos adicionales para cubrir cualquier aumento en los costes de env�o de los art�culos.

Informaci�n detallada sobre el vendedor