Iterated invariance principle for slowly mixing dynamical systems

Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1284-1304.

Matt Galton and Ian Melbourne

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.

pdf file, published version

Typo: In the second last line of the proof of Proposition 2.9, there is a mixing factor of n (i.e. 32 should be 32n). The statement and proof are correct.