A tourist's guide to regularity structures and singular stochastic PDEs
arXiv:2006.03524
Abstract
We give an essentially self-contained treatment of the fundamental analytic and algebraic features of regularity structures and its applications to the study of singular stochastic PDEs.
Final version, 97 pages. Improved presentation
References in corpus (30)
- Renormalising SPDEs in regularity structures
- Two interacting Hopf algebras of trees
- An analytic BPHZ theorem for regularity structures
- Pre-Lie algebras and the rooted trees operad
- Hopf algebras, from basics to applications to renormalization
- Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions
- Geometric stochastic heat equations
- The reconstruction theorem in Besov spaces
- A Rough Path Perspective on Renormalization
- A solution theory for quasilinear singular SPDEs
- Renormalization of Generalized KPZ equation
- Precise asymptotics: robust stochastic volatility models
- The motion of a random string
- The structure group for quasi-linear equations via universal enveloping algebras
- A diagram-free approach to the stochastic estimates in regularity structures
- Controlling Rough Paths
- Parabolic equations with rough coefficients and singular forcing
- Some recent progress in singular stochastic PDEs
- Paracontrolled calculus and regularity structures
- The support of singular stochastic PDEs
- An introduction to singular stochastic PDEs: Allen-Cahn equations, metastability and regularity structures
- An elementary proof of the reconstruction theorem
- Hairer's Reconstruction Theorem without Regularity Structures
- Renormalised singular stochastic PDEs
- Random models on regularity-integrability structures
- A flow approach to the generalized KPZ equation
- A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate
- A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate for singular modelled distributions
- An introduction to singular SPDEs
- Parabolic stochastic quantisation of the fractional model in the full subcritical regime