Probabilistic Approach to the Stochastic Burgers Equation

  • Massimiliano Gubinelli
  • Nicolas PerkowskiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)


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.


Stochastic Burgers equation Martingale problem Diffusions with distributional drift 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hausdorff Center for Mathematics & Institute for Applied MathematicsUniversität BonnBonnGermany
  2. 2.Institut für MathematikHumboldt–Universität zu BerlinBerlinGermany

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