Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation
Da Prato, Giuseppe ; Debussche, Arnaud
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998), p. 267-277 / Harvested from Biblioteca Digitale Italiana di Matematica
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We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup Pt⁢φ does exist for any bounded φ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.

Si considera un’equazione di Burgers stocastica. Si prova che il gradiente del semigruppo di transizione corrispondente Pt⁢φ esiste per ogni φ limitata e che può essere stimato con un opportuno peso esponenziale. Viene data un’applicazione ad una equazione di Hamilton-Jacobi che interviene in un problema di controllo stocastico.

Publié le : 1998-12-01
@article{RLIN_1998_9_9_4_267_0,
     author = {Giuseppe Da Prato and Arnaud Debussche},
     title = {Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {9},
     year = {1998},
     pages = {267-277},
     zbl = {0931.37036},
     mrnumber = {1722786},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1998_9_9_4_267_0}
}

Da Prato, Giuseppe; Debussche, Arnaud. Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998) pp. 267-277. http://gdmltest.u-ga.fr/item/RLIN_1998_9_9_4_267_0/

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