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.
Russo Francesco, Di Girolami Cristina (2020). About classical solutions of the path-dependent heat equation. RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 28(1), 35-62 [10.1515/rose-2020-2028].
About classical solutions of the path-dependent heat equation
Di Girolami Cristina
2020
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.| File | Dimensione | Formato | |
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