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arXiv · 1005.1781

Rough path stability of (semi-)linear SPDEs

Peter Friz·Harald Oberhauser
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Abstract

We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with its L\'evy area) as rough path noise the solution coincides with the standard variational solution of the SPDE.

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Peter Friz, Harald Oberhauser. 2010-05-11. Rough path stability of (semi-)linear SPDEs. https://arxiv.org/abs/1005.1781

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