hal-01145301 https://hal-ensta-paris.archives-ouvertes.fr//hal-01145301 https://hal-ensta-paris.archives-ouvertes.fr//hal-01145301v3/document https://hal-ensta-paris.archives-ouvertes.fr//hal-01145301v3/file/ComparisonViscosityOsaka2017_AcceptedDecember.pdf [INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions [UMA_ENSTA] Unité de Mathématiques Appliquées (UMA) [ENSTA-SACLAY] ENSTA-SACLAY [UNIV-PARIS-SACLAY] Université Paris-Saclay [ENSTA] ENSTA Paris [SORBONNE-UNIVERSITE] Sorbonne Université [UNIV-PARIS] Université de Paris [SU-TI] Sorbonne Université - Texte Intégral STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs Cosso, Andrea Russo, Francesco [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] UNDEFINED strong-viscosity solutions viscosity solutions backward stochastic differential equations path-dependent partial differential equations 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. 2019-03-08 2019-03-08 en