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Pré-Publication, Document De Travail Année : 2019

Viscosity solutions of path-dependent PDEs with randomized time

Résumé

We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we prove the two important results till now missing in the literature, namely, a general stability result and a comparison result for semicontinuous sub-/super-solutions. As an application, we prove the existence of viscosity solutions using the Perron method. Moreover, we connect viscosity solutions of path-dependent PDEs with viscosity solutions of partial differential equations on Hilbert spaces.
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Dates et versions

hal-02292995 , version 1 (20-09-2019)

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  • HAL Id : hal-02292995 , version 1

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Zhenjie Ren, Mauro Rosestolato. Viscosity solutions of path-dependent PDEs with randomized time. 2019. ⟨hal-02292995⟩
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