About classical solutions of the path-dependent heat equation.

Cristina Di Girolami and Francesco Russo

january, 2020

Publication type:

Paper in peer-reviewed journals

Journal:

Random Operators Stochastic Equations (ROSE), vol. 1, pp. 35-62

DOI:

10.1515/rose-2020-2028

HAL:

hal-01762783

arXiv:

1804.03845

Keywords :

Infinite dimensional analysis; Kolmogorov type equations; Path-dependent heat equation; Window Brownian motion;

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.

BibTeX:

@article{DiG-Rus-2020,
    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 },
    month={1},
    volume={1 },
    pages={35--62},
}