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- Title
About classical solutions of the path-dependent heat equation.
- Authors
Di Girolami, Cristina; Russo, Francesco
- 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 terminal conditions: the first one is given by a cylindrical not necessarily smooth random variable, the second one is a smooth generic functional.
- Subjects
HEAT equation; EXISTENCE theorems; BROWNIAN motion; CLASSICAL solutions (Mathematics); RANDOM variables
- Publication
Random Operators & Stochastic Equations, 2020, Vol 28, Issue 1, p35
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/rose-2020-2028