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Rough path stability of (semi-)linear SPDEs · arXivDesk

1005.1781May 11, 2010Final submitted version, to appear in PTRF. The previous title was "Rough path stability of SPDEs arising in non-linear filtering"

Rough path stability of (semi-)linear SPDEs

Peter Friz, Harald Oberhauser

Probability Analysis of PDEs

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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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The paper addresses: Rough path stability of (semi-)linear SPDEs.
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.

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Author comment: Final submitted version, to appear in PTRF. The previous title was "Rough path stability of SPDEs arising in non-linear filtering"