About classical solutions of the path-dependent heat equation.

january, 2020
Publication type:
Paper in peer-reviewed journals
Random Operators Stochastic Equations (ROSE), vol. 1, pp. 35-62
assets/images/icons/icon_arxiv.png 1804.03845
Keywords :
Infinite dimensional analysis; Kolmogorov type equations; Path-dependent heat equation; Window Brownian motion;
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.
    author={Cristina Di Girolami and Francesco Russo },
    title={About classical solutions of the path-dependent heat equation. },
    doi={10.1515/rose-2020-2028 },
    journal={Random Operators Stochastic Equations (ROSE) },
    year={2020 },
    volume={1 },