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

Toshiro Watanabe ()
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Toshiro Watanabe: The University of Aizu

Journal of Theoretical Probability, 2002, vol. 15, issue 3, 631-665

Abstract: 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.

Keywords: Shift self-similar additive random sequences; supercritical branching processes; b-decomposability; class OR (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1016267815166

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