About classical solutions of the path-dependent heat equation
Probability
2020-02-12 v3 Analysis of PDEs
Abstract
This paper investigates two existence theorems for the path-dependent heat equation, which is the Kolmogorov equation related to the window Brownian motion, considered as a C([--T, 0])-valued process. We concentrate on two general existence results of its classical solutions related to different classes of final conditions: the first one is given by a cylindrical non necessarily smooth r.v., the second one is a smooth generic functional.
Keywords
Cite
@article{arxiv.1804.03845,
title = {About classical solutions of the path-dependent heat equation},
author = {Cristina Di Girolami and Francesco Russo},
journal= {arXiv preprint arXiv:1804.03845},
year = {2020}
}