Viscosity solutions of path-dependent PDEs with randomized time

Zhenjie Ren; Mauro Rosestolato

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arXiv · 1806.07654

Viscosity solutions of path-dependent PDEs with randomized time

Zhenjie Ren·Mauro Rosestolato

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Abstract

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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BibTeX RIS

Zhenjie Ren, Mauro Rosestolato. 2018-06-20. Viscosity solutions of path-dependent PDEs with randomized time. https://arxiv.org/abs/1806.07654

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