• Corpus ID: 119287396

Martingale-driven approximations of singular stochastic PDEs

@article{Matetski2018MartingaledrivenAO,
title={Martingale-driven approximations of singular stochastic PDEs},
author={Konstantin Matetski},
journal={arXiv: Probability},
year={2018}
}
• K. Matetski
• Published 28 August 2018
• Mathematics, Computer Science
• arXiv: Probability
We define multiple stochastic integrals with respect to c\{a}dl\{a}g martingales and prove moment bounds and chaos expansions, which allow to work with them in a way similar to Wiener stochastic integrals. In combination with the discretization framework of Erhard and Hairer (2017), our results give a tool for proving convergence of interacting particle systems to stochastic PDEs using regularity structures. As examples, we prove convergence of martingale-driven discretizations of the $3… 5 Citations Some recent progress in singular stochastic PDEs. • Mathematics • 2019 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, Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity • Mathematics • 2018 Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an Some recent progress in singular stochastic partial differential equations • Mathematics Bulletin of the American Mathematical Society • 2019 Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent Stochastic PDE Limit of the Six Vertex Model • Mathematics Communications in Mathematical Physics • 2020 We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase Log‐Sobolev Inequality for the Continuum Sine‐Gordon Model • Mathematics Communications on Pure and Applied Mathematics • 2020 We derive a multiscale generalisation of the Bakry‐Émery criterion for a measure to satisfy a log‐Sobolev inequality. Our criterion relies on the control of an associated PDE well‐known in References SHOWING 1-10 OF 47 REFERENCES PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES • Mathematics Forum of Mathematics, Pi • 2015 We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough Renormalization Group and Stochastic PDEs We develop a renormalization group (RG) approach to the study of existence and uniqueness of solutions to stochastic partial differential equations driven by space-time white noise. As an example, we An analytic BPHZ theorem for regularity structures • Mathematics • 2016 We prove a general theorem on the stochastic convergence of appropriately renormalized models arising from nonlinear stochastic PDEs. The theory of regularity structures gives a fairly automated Discretisation of regularity structures • Computer Science, Mathematics Annales de l'Institut Henri Poincaré, Probabilités et Statistiques • 2019 A general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs and a "black box" describing the behaviour of the authors' discretised objects at scales below$\varepsilon \$ is introduced.
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