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International Conference on Stochastic Partial Differential Equations and Related Fields

SPDERF 2016: Stochastic Partial Differential Equations and Related Fields pp 515–527Cite as

Probabilistic Approach to the Stochastic Burgers Equation

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

Abstract

We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first review how to construct finite-dimensional diffusions with distributional drift. We then present the uniqueness result for the stationary martingale problem of (M. Gubinelli and N. Perkowski, Energy solutions of KPZ are unique. 2015, [18]), but we mainly emphasize the heuristic derivation and also we include a (very simple) extension of (M. Gubinelli and N. Perkowski, Energy solutions of KPZ are unique. 2015, [18]) to a non-stationary regime.

Financial support by the DFG via CRC 1060 (MG) and Research Unit FOR 2402 (NP) is gratefully acknowledged.

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Notes

  1. 1.

    The paper [16] is the revised and published version of [15].

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Author information

Authors and Affiliations

  1. Hausdorff Center for Mathematics & Institute for Applied Mathematics, Universität Bonn, Bonn, Germany

    Massimiliano Gubinelli

  2. Institut für Mathematik, Humboldt–Universität zu Berlin, Berlin, Germany

    Nicolas Perkowski

Authors
  1. Massimiliano Gubinelli
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  2. Nicolas Perkowski
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Corresponding author

Correspondence to Nicolas Perkowski .

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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Gubinelli, M., Perkowski, N. (2018). Probabilistic Approach to the Stochastic Burgers Equation. 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_35

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