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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
Article
  • 173 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

60H15 65M12 35L65 

Notes

Acknowledgements

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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