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.
Accepté le :
Publié le :
@article{CRMATH_2017__355_3_296_0, author = {Gassiat, Paul}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2017.01.021/} }
TY - JOUR AU - Gassiat, Paul TI - A stochastic Hamilton–Jacobi equation with infinite speed of propagation JO - Comptes Rendus. Mathématique PY - 2017 SP - 296 EP - 298 VL - 355 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2017.01.021/ DO - 10.1016/j.crma.2017.01.021 LA - en ID - CRMATH_2017__355_3_296_0 ER -
%0 Journal Article %A Gassiat, Paul %T A stochastic Hamilton–Jacobi equation with infinite speed of propagation %J Comptes Rendus. Mathématique %D 2017 %P 296-298 %V 355 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2017.01.021/ %R 10.1016/j.crma.2017.01.021 %G en %F CRMATH_2017__355_3_296_0
Gassiat, Paul. A stochastic Hamilton–Jacobi equation with infinite speed of propagation. Comptes Rendus. Mathématique, Tome 355 (2017) no. 3, pp. 296-298. doi : 10.1016/j.crma.2017.01.021. http://archive.numdam.org/articles/10.1016/j.crma.2017.01.021/
[1] 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] 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] 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)
Cité par Sources :