Paracontrolled quasilinear SPDEs
M. Furlan, M. Gubinelli
TL;DR
This paper develops a new non-linear paracontrolled calculus to handle and renormalize a class of singular stochastic partial differential equations, including some quasilinear variants of the 2D parabolic Anderson model.
Contribution
It introduces a novel non-linear paracontrolled calculus for renormalizing complex singular SPDEs, expanding the toolkit for quasilinear stochastic analysis.
Findings
Successfully renormalized certain quasilinear SPDEs
Extended paracontrolled calculus to non-linear cases
Applied method to 2D parabolic Anderson model
Abstract
We introduce a non-linear paracontrolled calculus and use it to renormalise a class of singular SPDEs including certain quasilinear variants of the periodic two dimensional parabolic Anderson model.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Advanced Mathematical Physics Problems · Advanced Mathematical Modeling in Engineering