Nous présentons un exemple d'équation d'Hamilton–Jacobi stochastique dont la vitesse de propagation est infinie dès que le signal ξ n'est pas à variation bornée.
We give an example of a stochastic Hamilton–Jacobi equation which has an infinite speed of propagation as soon as the driving signal ξ is not of bounded variation.
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Paul Gassiat 1
@article{CRMATH_2017__355_3_296_0, author = {Paul Gassiat}, title = {A stochastic {Hamilton{\textendash}Jacobi} equation with infinite speed of propagation}, journal = {Comptes Rendus. Math\'ematique}, pages = {296--298}, publisher = {Elsevier}, volume = {355}, number = {3}, year = {2017}, doi = {10.1016/j.crma.2017.01.021}, language = {en}, }
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/
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[3] 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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