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

## TL;DR

This paper establishes an almost sure invariance principle for non-autonomous holomorphic dynamical systems on complex projective space, showing they can be strongly approximated by Brownian motion for certain observables.

## Contribution

It introduces the first proof of an almost sure invariance principle for non-autonomous holomorphic dynamics on complex projective space.

## Key findings

- Almost sure invariance principle proven for non-autonomous systems
- Applicable to H"{o}lder continuous and DSH observables
- Strong approximation by Brownian motion achieved

## 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 $\Bbb{P}^k$ for H\"{o}lder continuous and DSH observables.