Some recent progress in singular stochastic PDEs

Abstract

Stochastic PDEs are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in defining, approximating and studying the properties of a few examples of such equations. We focus mainly on the dynamical Phi4 equation, KPZ equation and Parabolic Anderson Model, as well as touch on a few other equations which arise mainly in physics.

41 pages

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Cited by in corpus (7)

• Short time large deviations of the KPZ equation
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• A tourist's guide to regularity structures and singular stochastic PDEs
• KPZ on torus: Gaussian fluctuations
• Regularity structures for quasilinear singular SPDEs
• Gaussian fluctuations from the 2D KPZ equation
• Random models for singular SPDEs