A strong invariance principle for nonconventional sums

TL;DR

This paper establishes a strong invariance principle for complex sums involving multiple nonconventional terms of a stochastic process, advancing the theoretical understanding of their asymptotic behavior.

Contribution

It introduces a new strong invariance principle for sums with nonconventional indices, extending classical results to more complex sum structures.

Findings

Proves a strong invariance principle for nonconventional sums

Extends classical invariance results to complex sum structures

Provides theoretical tools for analyzing nonconventional sums

Abstract

This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$