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Dynamics of SPDEs Driven by a Small Fractional Brownian Motion with Hurst Parameter Larger than 1/2

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Stochastic Partial Differential Equations and Related Fields (SPDERF 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 229))

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Abstract

We consider mild solutions of an SPDE driven by a time dependent perturbation which is Hölder continuous with a Hölder exponent larger than 1/2. In particular, such a perturbation is given by a fractional Brownian motion with Hurst parameter larger than 1/2. The coefficient in front of this noise is an operator with bounded first and second derivatives. We formulate conditions such that the equation has a unique pathwise solution. Further we investigate the globally exponential stability of the trivial solution.

Dedicated to Michael Röckner on occasion of his Sixtieth Birthday.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut Für Mathematik in den Naturwissenschaften, Inselstr. 22, 04103, Leipzig, Germany

    L. H. Duc

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay disk, 10307, Hanoi, Vietnam

    M. J. Garrido-Atienza

  3. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Avda. Reina Mercedes, s/n, 41012, Sevilla, Spain

    B. Schmalfuß

  4. Institut für Mathematik, Friedrich Schiller Universität Jena, Ernst Abbe Platz 2, 77043, Jena, Germany

    L. H. Duc

Authors
  1. L. H. Duc
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  2. M. J. Garrido-Atienza
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  3. B. Schmalfuß
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Corresponding author

Correspondence to B. Schmalfuß .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Andreas Eberle

  2. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  3. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Walter Hoh

  4. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Moritz Kassmann

  5. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Wilhelm Stannat

  6. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

    Gerald Trutnau

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Duc, L.H., Garrido-Atienza, M.J., Schmalfuß, B. (2018). Dynamics of SPDEs Driven by a Small Fractional Brownian Motion with Hurst Parameter Larger than 1/2. In: Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-319-74929-7_11

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