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2011 Local Brownian property of the narrow wedge solution of the KPZ equation
Jeremy Quastel, Daniel Remenik
Author Affiliations +
Electron. Commun. Probab. 16: 712-719 (2011). DOI: 10.1214/ECP.v16-1678


Abstract. Let $H(t,x)$ be the Hopf-Cole solution at time t of the Kardar-Parisi-Zhang (KPZ) equation starting with narrow wedge initial condition, i.e. the logarithm of the solution of the multiplicative stochastic heat equation starting from a Dirac delta. Also let $H^{eq}(t,x)$ be the solution at time $t$ of the KPZ equation with the same noise, but with initial condition given by a standard two-sided Brownian motion, so that $H^{eq}(t,x)-H^{eq}$ is locally of finite variation. Using the same ideas we also show that if the KPZ equation is started with a two-sided Brownian motion plus a Lipschitz function then the solution stays in this class for all time.


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Jeremy Quastel. Daniel Remenik. "Local Brownian property of the narrow wedge solution of the KPZ equation." Electron. Commun. Probab. 16 712 - 719, 2011.


Accepted: 20 November 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1243.60054
MathSciNet: MR2861435
Digital Object Identifier: 10.1214/ECP.v16-1678

Primary: 60H15
Secondary: 60K35, 82C22


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