We prove asymptotic convergence results for some analytical expansions of solutions of 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.
Andrea Pascucci, Stefano Pagliarani (2014). Asymptotic expansions for degenerate parabolic equations. COMPTES RENDUS MATHÉMATIQUE, 352(12), 1011-1016 [10.1016/j.crma.2014.09.024].
Asymptotic expansions for degenerate parabolic equations
PASCUCCI, ANDREA;PAGLIARANI, STEFANO
2014
Abstract
We prove asymptotic convergence results for some analytical expansions of solutions of 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.File in questo prodotto:
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