Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions View Full Text


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Article Info

DATE

2020-11-03

AUTHORS

Rainer Buckdahn, Christian Keller, Jin Ma, Jianfeng Zhang

ABSTRACT

We study fully nonlinear second-order (forward) stochastic PDEs. They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework. For the most general fully nonlinear case, we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions. Our notion of viscosity solutions is equivalent to the alternative using semi-jets. Next, we prove basic properties such as consistency, stability, and a partial comparison principle in the general setting. If the diffusion coefficient is semilinear (i.e, linear in the gradient of the solution and nonlinear in the solution; the drift can still be fully nonlinear), we establish a complete theory, including global existence and a comparison principle. More... »

PAGES

7

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s41546-020-00049-8

DOI

http://dx.doi.org/10.1186/s41546-020-00049-8

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https://app.dimensions.ai/details/publication/pub.1132292484


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