Singular stochastic PDEs

2014/03/25 by Martin Hairer, Hairer, Martin
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H15 #81S20 #82C28 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1403.6353

openalex publication_date 2014/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This problem can be addressed within the framework of the recently developed theory of "regularity structures", which allows to describe candidate solutions locally by a "jet", but where the usual Taylor polynomials are replaced by a sequence of custom-built objects. In order to illustrate the theory, we focus on the particular example of the Kardar-Parisi-Zhang equation, a popular model for interface propagation.

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