Viscosity solutions of path-dependent PDEs with randomized time
Probability
2018-06-21 v1
Abstract
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.
Cite
@article{arxiv.1806.07654,
title = {Viscosity solutions of path-dependent PDEs with randomized time},
author = {Zhenjie Ren and Mauro Rosestolato},
journal= {arXiv preprint arXiv:1806.07654},
year = {2018}
}