%0 Unpublished work
%T STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs
%+ Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
%+ Unité de Mathématiques Appliquées (UMA)
%A Cosso, Andrea
%A Russo, Francesco
%8 2018-11-17
%D 2018
%K strong-viscosity solutions
%K viscosity solutions
%K backward stochastic differential equations
%K path-dependent partial differential equations
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.
%G English
%Z "FMJH Program Gaspard Monge in optimization and operation research'' (Project 2014-1607H).
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301v2/document
%2 https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301v2/file/ComparisonViscosityOsaka2017_AcceptedDecember.pdf
%L hal-01145301
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301