Lacunary Series and Strong Approximation
István Berkes
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.
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.
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Taxonomy
TopicsProbability and Risk Models · Advanced Banach Space Theory · Stochastic processes and financial applications