An inductive approach to stochastic estimates for the φ⁴₂-equation with correlated coefficient field

2025/09/14 by Nicolas Clozeau, Clozeau, Nicolas
Economics, Econometrics and Finance · #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2509.11309

openalex publication_date 2025/09/14 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We develop an inductive approach to obtaining stochastic estimates for the φ⁴₂-equation when the coefficient field is correlated with the driving noise. Our method is based on (infinite-dimensional) Gaussian integration by parts with respect to Wick products of Gaussian random variables (more precisely, mollifications of space-time white noise)

Citations

• Renormalisation of singular SPDEs with Correlated Coefficients
• Renormalised Models for Variable Coefficient Singular SPDEs
• Random models on regularity-integrability structures
• Canonical solutions to non-translation invariant singular SPDEs
• Characterizing models in regularity structures: a quasilinear case
• A diagram-free approach to the stochastic estimates in regularity structures
• An analytic BPHZ theorem for regularity structures
• Spectral Gap for the Stochastic Quantization Equation on the 2-dimensional Torus
• A class of growth models rescaling to KPZ
• Paracontrolled distributions and singular PDEs
• Estimation of the Mean of a Multivariate Normal Distribution

Cited by

• Renormalisation of singular SPDEs with Correlated Coefficients

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