Stochastic evolution equations with rough boundary noise
Probability
2023-10-17 v3 Analysis of PDEs
Dynamical Systems
Abstract
We investigate the pathwise well-posedness of stochastic evolution equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for . Combining the controlled rough path approach with the theory of extrapolation operators, we establish global existence of solutions and flows for such equations. For Dirichlet boundary noise we obtain similar results in the Young regime.
Cite
@article{arxiv.2209.10348,
title = {Stochastic evolution equations with rough boundary noise},
author = {Alexandra Neamtu and Tim Seitz},
journal= {arXiv preprint arXiv:2209.10348},
year = {2023}
}
Comments
To appear in Partial Differential Equations and Applications, 30 pages