English

Iterated invariance principle for slowly mixing dynamical systems

Dynamical Systems 2022-05-30 v2

Abstract

We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals. We illustrate this with examples of deterministic fast-slow systems where our iterated invariance principle yields convergence to a stochastic differential equation.

Keywords

Cite

@article{arxiv.2004.13398,
  title  = {Iterated invariance principle for slowly mixing dynamical systems},
  author = {Matt Galton and Ian Melbourne},
  journal= {arXiv preprint arXiv:2004.13398},
  year   = {2022}
}

Comments

Final version to appear in Ann. Inst. H. Poincare Probab. Statist. Only minor changes from v1

R2 v1 2026-06-23T15:08:51.467Z