Probability Theory and Related Fields

, Volume 173, Issue 3–4, pp 1063–1098 | Cite as

Regularization by noise for stochastic Hamilton–Jacobi equations

  • Paul GassiatEmail author
  • Benjamin Gess


We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path \(L^{\infty }\) bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.


Stochastic Hamilton–Jacobi equations; regularization by noise Reflected SDE Stochastic p-Laplace equation Stochastic total variation flow 

Mathematics Subject Classification

60H15 65M12 35L65 



The work of PG was supported by the ANR, via the project ANR-16-CE40- 0020-01. The work of BG was supported by the DFG through CRC 1283.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CeremadeUniversité de Paris-DauphineParis cedex 16France
  2. 2.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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