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The KPZ Equation on the Real Line

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arxiv 1808.00354 v2 pith:OSA3Y5IX submitted 2018-08-01 math.PR math.AP

Nicolas Perkowski , Tommaso Cornelis Rosati This is my paper · ORCID
classification math.PRmath.AP
keywords analysisequationlinerealsolutionspaceboundscharacterisation
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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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  1. Stationary Directed Polymers and Energy Solutions of the Burgers Equation

    math.PR 2019-08 conditional novelty 6.0 of 10

    The stationary O'Connell-Yor polymer increments converge to energy solutions of the stochastic Burgers equation without using the Cole-Hopf transform.

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