Almost Sure Invariance Principle for non-autonomous holomorphic dynamics in ${\mathbb{P}}^k$

Abstract

We prove almost sure invariance principle, a strong form of approximation by Brownian motion, for non-autonomous holomorphic dynamical systems on complex projective space ${\mathbb{P}}^k$ for Hölder continuous and DSH observables.

v2. Minor revisions, v3. Statement of Theorem 1.2 is slightly improved by relaxing the assumption on the growth rate of the variances. Incorporating Referee comments. To appear in Comform. Geom. Dyn

References in corpus (2)

• Exponential estimates for plurisubharmonic functions and stochastic dynamics
• Martingale-coboundary decomposition for families of dynamical systems