A pathwise analysis of stochastic evolution equations with locally monotone operators

Paper Title:

On Young regimes for locally monotone SPDEs

Published on:

2 May 2024

Primary Category:

Probability

Paper Authors:

Florian Bechtold,

Jörn Wichmann

Bullets

Key Details

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Combines monotone operator theory and Besov rough path analysis

•

Applies to various locally monotone operators and driving signals

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Identifies noise regimes assuring existence and sometimes uniqueness

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Captures regularization by noise through local time of oscillator

Explore the topics in this paper

besov rough path analysis

monotone operator theory

nonlinear pdes

regularity structures

stochastic evolution equations

AI generated summary

A pathwise analysis of stochastic evolution equations with locally monotone operators

We establish global existence of weak solutions to stochastic evolution equations on a Gelfand triple with locally monotone operators and sufficiently regular driving signals. Our analysis combines monotone operator theory with recent advances in Besov rough path analysis, requiring no probabilistic structure. This allows treating various operators and signals, including p-Laplace, porous medium, shear-thickening fluids, additive/multiplicative Young integrals, and translated integrals arising in regularization by noise.