Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 117, 56 pp.
The KPZ equation on the real line
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.
Electron. J. Probab., Volume 24 (2019), paper no. 117, 56 pp.
Received: 18 February 2019
Accepted: 8 September 2019
First available in Project Euclid: 29 October 2019
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Perkowski, Nicolas; Cornelis Rosati, Tommaso. The KPZ equation on the real line. Electron. J. Probab. 24 (2019), paper no. 117, 56 pp. doi:10.1214/19-EJP362. https://projecteuclid.org/euclid.ejp/1572314777