[Expansions asymptotiques pour équations paraboliques dégénérées]
On démontre des résultats de convergence asymptotique pour certaines expansions analytiques de solutions d'équations aux dérivés partielles dégénérées avec des applications aux mathématiques financières. En particulier, on combine des estimations d'erreur à temps petit, globales dans l'espace, obtenues précédemment dans le cas uniformément parabolique, avec quelques bornes a priori sur de « courts cylindres », et on attend la convergence asymptotique à temps petit de la solution approchée dans le cas parabolique dégénéré.
We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short-time asymptotic convergence of the approximate solution in the degenerate parabolic case.
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@article{CRMATH_2014__352_12_1011_0,
author = {Stefano Pagliarani and Andrea Pascucci},
title = {Asymptotic expansions for degenerate parabolic equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1011--1016},
publisher = {Elsevier},
volume = {352},
number = {12},
year = {2014},
doi = {10.1016/j.crma.2014.09.024},
language = {en},
}
Stefano Pagliarani; Andrea Pascucci. Asymptotic expansions for degenerate parabolic equations. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1011-1016. doi : 10.1016/j.crma.2014.09.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.024/
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