Escape Rates for Multidimensional Shift Self-similar Additive Sequences

Toshiro Watanabe ()
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Toshiro Watanabe: Univ. of Aizu.

Journal of Theoretical Probability, 2016, vol. 29, issue 3, 896-921

Abstract: Abstract 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 logarithm for strictly stable Lévy processes on $$\mathbb {R}^d$$ R d and independent Brownian motions are given.

Keywords: Shift self-similar additive sequence; Stationary sequence of OU type; $$b$$ b -Decomposable distribution; 60G18; 60G10; 60G50 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0599-7

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