# Weak invariance principle in Besov spaces for stationary martingale differences

## TL;DR

This paper extends the classical Donsker weak invariance principle to Besov spaces, analyzing polygonal line processes from stationary martingale differences and i.i.d. variables, demonstrating the optimality of the results.

## Contribution

It introduces a new invariance principle in Besov spaces for stationary martingale differences, expanding the theoretical framework beyond classical settings.

## Key findings

- Extension of Donsker's principle to Besov spaces
- Optimality of the derived results
- Applicability to stationary martingale differences and i.i.d. variables

## Abstract

The classical Donsker weak invariance principle is extended to a Besov spaces framework. Polygonal line processes build from partial sums of stationary martingale differences as well independent and identically distributed random variables are considered. The results obtained are shown to be optimal.