About classical solutions of the path-dependent heat equation.
january, 2020
Publication type:
Paper in peer-reviewed journals
Journal:
Random Operators Stochastic Equations (ROSE), vol. 1, pp. 35-62
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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}, }