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Escape Rates for Multidimensional Shift Self-similar Additive Sequences

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  • Toshiro Watanabe

    (Univ. of Aizu.)

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.

Suggested Citation

  • Toshiro Watanabe, 2016. "Escape Rates for Multidimensional Shift Self-similar Additive Sequences," Journal of Theoretical Probability, Springer, vol. 29(3), pages 896-921, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0599-7
    DOI: 10.1007/s10959-015-0599-7
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    References listed on IDEAS

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    1. Toshiro Watanabe, 2002. "Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes," Journal of Theoretical Probability, Springer, vol. 15(3), pages 631-665, July.
    2. Makoto Maejima & Ken-iti Sato, 1999. "Semi-Selfsimilar Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 347-373, April.
    3. Toshiro Watanabe, 2000. "Continuity Properties of Distributions with Some Decomposability," Journal of Theoretical Probability, Springer, vol. 13(1), pages 169-191, January.
    Full references (including those not matched with items on IDEAS)

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