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Quasi-generalised KPZ equation

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arxiv 2401.13620 v2 pith:ELAEAVNO submitted 2024-01-24 math.PR math.AP

Yvain Bruned , Máté Gerencsér , Usama Nadeem This is my paper · ORCID
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keywords equationquasi-generalisedrenormalisedsolutionalgebraiccasechaincombined
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We derive the renormalised equation for the quasi-generalised KPZ equation with space-time white noise. We complement the program initiated by Gerencs\'er and Hairer for solving quasi-linear equations using regularity structures by an algebraic machinery that gives a systematic tool to remove non-local counterterms and provide a precise expression of the renormalised equation that is consistent with the semilinear case. The solution theory satisfies the chain rule and a natural notion of It\^o isometry, which can be combined to obtain global in time solution.

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