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We obtain a strong invariance principle for nonconventional sums and applyingthis result we derive for them a version of the law of iterated logarithm, aswell as an almost sure central limit theorem. Among motivations for suchresults are their applications to multiple recurrence for stochastic processesand dynamical systems.

Strong Approximations for Nonconventional Sums with Applications to Law of Iterated Logarithm and Almost Sure Central Limit Theorem