A vector-valued almost sure invariance principle for random expanding on average cocycles
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Publication:6375598
DOI10.1007/S10955-023-03067-WarXiv2108.08714MaRDI QIDQ6375598
Davor Dragičević, Yeor Hafouta, Julien Sedro
Publication date: 19 August 2021
Abstract: We obtain a quenched vector-valued almost sure invariance principle (ASIP) for random expanding on average cocycles. This is achieved by combining the adapted version of Gou"{e}zel's approach for establishing ASIP and the recent construction of the so-called adapted norms, which in some sense eliminate the non-uniformity of the decay of correlations. For real-valued observables, we also show that the martingale approximation technique is applicable in our setup, and that it yields the ASIP with better error rates. Finally, we present an example showing the necessity of a scaling condition, answering a question of the first and third authors.
Dynamical systems and their relations with probability theory and stochastic processes (37A50) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Generation, random and stochastic difference and differential equations (37H10) Functional limit theorems; invariance principles (60F17)
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