Non-linear rough heat equations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-06

AUTHORS

A. Deya, M. Gubinelli, S. Tindel

ABSTRACT

This article is devoted to define and solve an evolution equation of the form dyt = Δytdt + dXt (yt), where Δ stands for the Laplace operator on a space of the form , and X is a finite dimensional noisy nonlinearity whose typical form is given by , where each x = (x(1), … , x(N)) is a γ-Hölder function generating a rough path and each fi is a smooth enough function defined on . The generalization of the usual rough path theory allowing to cope with such kind of system is carefully constructed. More... »

PAGES

97-147

References to SciGraph publications

  • 1983. Semigroups of Linear Operators and Applications to Partial Differential Equations in NONE
  • 2003. An Introduction to Rough Paths in SÉMINAIRE DE PROBABILITÉS XXXVII
  • 2000-03. Nonlinear stochastic wave and heat equations in PROBABILITY THEORY AND RELATED FIELDS
  • 2011-05. The rough path associated to the multidimensional analytic fBm with any Hurst parameter in COLLECTANEA MATHEMATICA
  • 2006-12. Young Integrals and SPDEs in POTENTIAL ANALYSIS
  • 2012. Some Differential Systems Driven by a fBm with Hurst Parameter Greater than 1/4 in STOCHASTIC ANALYSIS AND RELATED TOPICS
  • 1998-07. Integration with respect to fractal functions and stochastic calculus. I in PROBABILITY THEORY AND RELATED FIELDS
  • 1986. An introduction to stochastic partial differential equations in ÉCOLE D'ÉTÉ DE PROBABILITÉS DE SAINT FLOUR XIV - 1984
  • 2003-10. Stochastic evolution equations with fractional Brownian motion in PROBABILITY THEORY AND RELATED FIELDS
  • 1999-12. Lipschitz Functions and Fractional Sobolev Spaces in POTENTIAL ANALYSIS
  • 1995. The Malliavin Calculus and Related Topics in NONE
  • 2002-01. Stochastic analysis, rough path analysis and fractional Brownian motions in PROBABILITY THEORY AND RELATED FIELDS
  • 1936-12. An inequality of the Hölder type, connected with Stieltjes integration in ACTA MATHEMATICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00440-011-0341-z

    DOI

    http://dx.doi.org/10.1007/s00440-011-0341-z

    DIMENSIONS

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