VISCOSITY SOLUTIONS OF PATH-DEPENDENT PDEs WITH RANDOMIZED TIME
SIAM JOURNAL ON MATHEMATICAL ANALYSIS(2020)
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 [I. Ekren et al., Ann. Probab., 42 (2014), pp. 204-236]. With the new definition, we prove the two important results, until now missing in the literature, namely, a general stability result and a comparison result for semicontinuous sub-/supersolutions. 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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Key words
viscosity solution,path-dependent partial differential equations,partial differential equations in infinite dimension
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