Iterated invariance principle for slowly mixing dynamical systems
arXiv:2004.13398
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.
Final version to appear in Ann. Inst. H. Poincare Probab. Statist. Only minor changes from v1