The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.
L'equazione di Hamilton-Jacobi-Bellman corrispondente a un'ampia classe di problemi di controllo distribuiti viene ridotta a una equazione parabolica lineare avente una soluzione regolare. Viene inoltre ottenuta una formula per la derivata prima della soluzione.
@article{RLIN_1997_9_8_3_183_0,
author = {Giuseppe Da Prato and Jerzy Zabczyk},
title = {Differentiability of the Feynman-Kac semigroup and a control application},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {8},
year = {1997},
pages = {183-188},
zbl = {0910.93025},
mrnumber = {1611613},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1997_9_8_3_183_0}
}
Da Prato, Giuseppe; Zabczyk, Jerzy. Differentiability of the Feynman-Kac semigroup and a control application. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 8 (1997) pp. 183-188. http://gdmltest.u-ga.fr/item/RLIN_1997_9_8_3_183_0/
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