Iterated invariance principle for slowly mixing dynamical systems

DOI10.1214/21-AIHP1190zbMATH Open1526.37010arXiv2004.13398MaRDI QIDQ6339579

Publication date: 28 April 2020

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.

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ergodicity, mixing, rates of mixing (37A25) Stochastic integrals (60H05) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Functional limit theorems; invariance principles (60F17)

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