Random processes and Central Limit Theorem in Besov spaces

TL;DR

This paper explores conditions under which random processes belong to Besov spaces and establishes the Central Limit Theorem within these spaces, also analyzing tail behavior of sums of independent random vectors.

Contribution

It provides new sufficient conditions for random processes to be in Besov spaces and extends the CLT to these function spaces, including tail behavior analysis.

Findings

Established criteria for process membership in Besov spaces

Proved CLT in Besov spaces under new conditions

Analyzed non-asymptotic tail bounds for sums of random vectors

Abstract

We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces. Main apparatus is the theory of mixed (anisotropic) Lebesgue-Riesz spaces, in particular so-called permutation inequality.