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Journal Articles Random Operators and Stochastic Equations Year : 2020

About classical solutions of the path-dependent heat equation

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.
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Dates and versions

hal-01762783 , version 1 (10-04-2018)
hal-01762783 , version 2 (08-12-2018)
hal-01762783 , version 3 (02-02-2020)

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Cite

Cristina Di Girolami, Francesco Russo. About classical solutions of the path-dependent heat equation. Random Operators and Stochastic Equations, 2020, 1, pp.35-62. ⟨10.1515/rose-2020-2028⟩. ⟨hal-01762783v3⟩
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