Rough path stability of (semi-)linear SPDEs |
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| Authors: | Peter Friz Harald Oberhauser |
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| Institution: | 1. WIAS, Mohrenstrasse 39, 10117, Berlin, Germany
2. Institut für Mathematik, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany
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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 Lévy area) as rough path noise the solution coincides with the standard variational solution of the SPDE. |
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