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First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on $$\mathbb {R}^d$$ R d is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary sequences of OU type are solved. Some applications to laws of the iterated...
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