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Article overview
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Comparison of viscosity solutions of fully nonlinear degenerate parabolic Path-dependent PDEs | | Zhenjie Ren
; Nizar Touzi
; Jianfeng Zhang
; | | Date: |
18 Nov 2015 | | Abstract: | We prove a comparison result for viscosity solutions of (possibly degenerate)
parabolic fully nonlinear path-dependent PDEs. In contrast with the previous
result in Ekren, Touzi & Zhang, our conditions are easier to check and allow
for the degenerate case, thus including first order path-dependent PDEs. Our
argument follows the regularization method as introduced by Jensen, Lions &
Souganidis in the corresponding finite-dimensional PDE setting. The present
argument significantly simplifies the comparison proof in Ekren, Touzi & Zhang,
but requires an $L^p-$type of continuity (with respect to the path) for the
viscosity semi-solutions and for the nonlinearity defining the equation. | | Source: | arXiv, 1511.5910 | | Services: | Forum | Review | PDF | Favorites | |
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