Open Access
2019 The KPZ equation on the real line
Nicolas Perkowski, Tommaso Cornelis Rosati
Electron. J. Probab. 24: 1-56 (2019). DOI: 10.1214/19-EJP362


We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our main tool for extending the analysis on the torus to the full space is a comparison result that gives quantitative upper and lower bounds for the solution. We then extend our analysis to provide a path-by-path construction of the random directed polymer measure on the real line and we derive a variational characterisation of the solution to the KPZ equation.


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Nicolas Perkowski. Tommaso Cornelis Rosati. "The KPZ equation on the real line." Electron. J. Probab. 24 1 - 56, 2019.


Received: 18 February 2019; Accepted: 8 September 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142911
MathSciNet: MR4029420
Digital Object Identifier: 10.1214/19-EJP362

Primary: 35R60 , 60H15

Keywords: Comparison principle , KPZ equation , Paracontrolled distributions , Singular SPDEs

Vol.24 • 2019
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