Limit Theorems for Multiplicative Processes

Quansheng Liu (), Emmanuel Rio () and Alain Rouault ()
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Quansheng Liu: Université de Bretagne-Sud
Emmanuel Rio: Université de Bretagne-Sud
Alain Rouault: Université de Bretagne-Sud

Journal of Theoretical Probability, 2003, vol. 16, issue 4, 971-1014

Abstract: Abstract Let W be a non-negative random variable with EW=1, and let {W i } be a family of independent copies of W, indexed by all the finite sequences i=i 1⋅⋅⋅i n of positive integers. For fixed r and n the random multiplicative measure μ n r has, on each r-adic interval $$A_{i_1 ...i_n }^r $$ at nth level, the density $$W_{i_1 } \cdot \cdot \cdot W_{i_1 \ldots i_n } $$ with respect to the Lebesgue measure on [0,1]. If EW log W

Keywords: self-similar cascades; Mandelbrot's martingales; random measures; laws of large numbers; functional central limit theorems; functional law of the iterated logarithm; large deviations (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/B:JOTP.0000012003.49768.f6

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