Multidimensional rates for a deterministic weak invariance principle
Nicol貌 Paviato (Warwick)
A chaotic dynamical system often gives rise to interesting statistical properties, such as the strong law of large numbers and the central limit theorem. In this talk, we will glimpse into the world of smooth ergodic theory, recalling limit theorems for random variables and processes which are generated by a deterministic system. In particular, we will present new rates of convergence to a multidimensional Brownian motion for nonuniformly expanding maps and semiflows. These results were obtained using martingale techniques and a new martingale-coboundary decomposition in the style of Gordin.
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