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Viscosity solutions of path-dependent PDEs with randomized time

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1806.07654.pdf (311.0Kb)
Date
2018-06
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
06-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Dewey
Probabilités et mathématiques appliquées
Sujet
Viscosity solution; Path-dependent partial differential equations; Partial differential equations in infinite dimension.
URI
https://basepub.dauphine.fr/handle/123456789/19861
Collections
  • CEREMADE : Publications
Metadata
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Author
Ren, Zhenjie
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rosestolato, Mauro
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Type
Document de travail / Working paper
Item number of pages
34
Abstract (EN)
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we prove the two important results till now missing in the literature, namely, a general stability result and a comparison result for semicontinuous sub-/super-solutions. As an application, we prove the existence of viscosity solutions using the Perron method. Moreover, we connect viscosity solutions of path-dependent PDEs with viscosity solutions of partial differential equations on Hilbert spaces.

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