# Lacunary Series and Strong Approximation

## TL;DR

This paper uses strong approximation to prove new limit theorems for lacunary series with conditionally independent sequences.

## Contribution

The novelty lies in applying strong approximation to lacunary series in a permutation-invariant and uniform manner.

## Key findings

- Uniform limit theorems are established for lacunary series using strong approximation.
- Permutation-invariant results are derived for conditionally independent sequences in lacunary series.

## Abstract

Strong approximation, introduced by Strassen (1964), is one of the most powerful methods to prove limit theorems in probability and statistics. In this paper we use strong approximation of lacunary series with conditionally independent sequences to prove uniform and permutation-invariant limit theorems for such series.