Rough path stability of (semi-)linear SPDEs View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-02-08

AUTHORS

Peter Friz, Harald Oberhauser

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. More... »

PAGES

401-434

References to SciGraph publications

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  • 2006-09-12. Wong-Zakai approximations of stochastic evolution equations in JOURNAL OF EVOLUTION EQUATIONS
  • 2005. Continuity of the Itô-Map for Holder Rough Paths with Applications to the Support Theorem in Holder Norm in PROBABILITY AND PARTIAL DIFFERENTIAL EQUATIONS IN MODERN APPLIED MATHEMATICS
  • 2007. Differential Equations Driven by Rough Paths, École d'Été de Probabilités de Saint-Flour XXXIV - 2004 in NONE
  • 2002-01. Stochastic analysis, rough path analysis and fractional Brownian motions in PROBABILITY THEORY AND RELATED FIELDS
  • 2007. A Concise Course on Stochastic Partial Differential Equations in NONE
  • 1996-06. Wong-Zakai approximations for stochastic differential equations in ACTA APPLICANDAE MATHEMATICAE
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    URI

    http://scigraph.springernature.com/pub.10.1007/s00440-013-0483-2

    DOI

    http://dx.doi.org/10.1007/s00440-013-0483-2

    DIMENSIONS

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