Holderian weak invariance principle for stationary mixing sequences

TL;DR

This paper establishes conditions under which stationary mixing sequences satisfy the weak invariance principle in Hölder spaces, using inequalities and truncation techniques.

Contribution

It introduces sufficient mixing conditions for the weak invariance principle in Hölder spaces, extending previous results to various mixing types.

Findings

Weak invariance principle holds under certain mixing conditions.

Fuk-Nagaev inequalities are effective tools for analysis.

Results apply to strong, ρ-, and τ-dependent sequences.

Abstract

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in H\"older spaces. Strong mixing and $\rho$-mixing conditions are investigated as well as $\tau$-dependent sequences. The main tools are Fuk-Nagaev type inequalities for mixing sequences and a truncation argument.