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Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes

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  • Toshiro Watanabe

    (The University of Aizu)

Abstract

Natural examples of increasing shift self-similar additive random sequences are constructed, which are associated with supercritical branching processes. The rate of growth and the distributional properties of them are studied in terms of the offspring distributions of the supercritical branching processes. The results are applied to two types of laws of the iterated logarithm for a Brownian motion on the unbounded Sierpinski gasket. An extension of the Bingham–Doney–de Meyer theorem on the limits of supercritical branching processes is also proved.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:3:d:10.1023_a:1016267815166
    DOI: 10.1023/A:1016267815166
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    References listed on IDEAS

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    1. Makoto Maejima & Ken-iti Sato, 1999. "Semi-Selfsimilar Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 347-373, April.
    2. Toshiro Watanabe, 2000. "Continuity Properties of Distributions with Some Decomposability," Journal of Theoretical Probability, Springer, vol. 13(1), pages 169-191, January.
    3. Maejima, Makoto & Sato, Ken-iti & Watanabe, Toshiro, 2000. "Distributions of selfsimilar and semi-selfsimilar processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 395-401, May.
    4. Arous, Gerard Ben & Kumagai, Takashi, 2000. "Large deviations for Brownian motion on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 225-235, February.
    5. Wolfe, Stephen James, 1983. "Continuity properties of decomposable probability measures on euclidean spaces," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 534-538, December.
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    Cited by:

    1. Toshiro Watanabe, 2016. "Escape Rates for Multidimensional Shift Self-similar Additive Sequences," Journal of Theoretical Probability, Springer, vol. 29(3), pages 896-921, September.

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