A strong invariance principle for nonconventional sums

preprint2010arXivOpen access

Abstract

This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form ∑n=1[Nt]F(X(n),X(2n),...,X(kn),X(qk+1(n)),X(qk+2(n)),...,X(qℓ(n)))\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)

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