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Rough path stability of (semi-)linear SPDEs (1005.1781v3)
Published 11 May 2010 in math.PR and math.AP
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.