Comptes Rendus
no. 3
Partial differential equations
A stochastic Hamilton–Jacobi equation with infinite speed of propagation

Presented by: the Editorial Board

Paul Gassiat1
1 Ceremade, Université Paris-Dauphine, PSL Research University, place du Maréchal-de-Lattre-de-Tassigny, 75775, Paris cedex 16, France
Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 296-298.

We give an example of a stochastic Hamilton–Jacobi equation du=H(Du)dξ which has an infinite speed of propagation as soon as the driving signal ξ is not of bounded variation.

Nous présentons un exemple d'équation d'Hamilton–Jacobi stochastique du=H(Du)dξ dont la vitesse de propagation est infinie dès que le signal ξ n'est pas à variation bornée.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.01.021

Paul Gassiat 1

1 Ceremade, Université Paris-Dauphine, PSL Research University, place du Maréchal-de-Lattre-de-Tassigny, 75775, Paris cedex 16, France 
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     title = {A stochastic {Hamilton{\textendash}Jacobi} equation with infinite speed of propagation},
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Paul Gassiat. A stochastic Hamilton–Jacobi equation with infinite speed of propagation. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 296-298. doi : 10.1016/j.crma.2017.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.021/

[1] L.C. Evans; P.E. Souganidis Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations, Indiana Univ. Math. J., Volume 33 (1984) no. 5, pp. 773-797

[2] P.-L. Lions; P.E. Souganidis Fully nonlinear stochastic partial differential equations: non-smooth equations and applications, C. R. Acad. Sci. Paris, Ser. I, Volume 327 (1998) no. 8, pp. 735-741 | DOI

[3] P.E. Souganidis Fully nonlinear first- and second-order stochastic partial differential equations, Lecture Notes from the CIME Summer School “Singular random dynamics”, 2016 http://php.math.unifi.it/users/cime/Courses/2016/course.php?codice=20162 (available at)

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