Rough path stability of (semi-)linear SPDEs

Springer Science and Business Media LLC - Tập 158 - Trang 401-434 - 2013
Peter Friz1,2, Harald Oberhauser2
1WIAS, Berlin, Germany
2Institut für Mathematik, TU Berlin, Berlin, Germany

Tóm tắt

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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