hal-01145301
https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301
https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301v2/document
https://hal-ensta-paris.archives-ouvertes.fr/hal-01145301v2/file/ComparisonViscosityOsaka2017_AcceptedDecember.pdf
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.
2018-11-17
2018-11-17
en