Strong-viscosity Solutions: Semilinear Parabolic PDEs and Path-dependent PDEs

Abstract

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.

arXiv admin note: text overlap with arXiv:1401.5034

References in corpus (2)

• Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs
• Weak Functional Itô Calculus and Applications

Cited by in corpus (5)

• Weak Functional Itô Calculus and Applications
• A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs
• G{â}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes
• Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs
• A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps