Electronic Journal of Probability

The KPZ equation on the real line

Nicolas Perkowski and Tommaso Cornelis Rosati

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 117, 56 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1572314777

Digital Object Identifier
doi:10.1214/19-EJP362

Mathematical Reviews number (MathSciNet)
MR4029420

Zentralblatt MATH identifier
07142911

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Keywords
KPZ equation singular SPDEs paracontrolled distributions comparison principle

Rights
Creative Commons Attribution 4.0 International License.

Citation

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


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