Rough path stability of (semi-)linear SPDEs
arXiv:1005.1781
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.
Final submitted version, to appear in PTRF. The previous title was "Rough path stability of SPDEs arising in non-linear filtering"