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Limit Theorems for Multiplicative Processes

Author

Listed:
  • Quansheng Liu

    (Université de Bretagne-Sud)

  • Emmanuel Rio

    (Université de Bretagne-Sud)

  • Alain Rouault

    (Université de Bretagne-Sud)

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

Suggested Citation

  • Quansheng Liu & Emmanuel Rio & Alain Rouault, 2003. "Limit Theorems for Multiplicative Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 971-1014, October.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:4:d:10.1023_b:jotp.0000012003.49768.f6
    DOI: 10.1023/B:JOTP.0000012003.49768.f6
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    References listed on IDEAS

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    1. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.
    2. Liu, Quansheng, 2001. "Asymptotic properties and absolute continuity of laws stable by random weighted mean," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 83-107, September.
    3. Liu, Quansheng, 2000. "On generalized multiplicative cascades," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 263-286, April.
    4. Eichelsbacher, Peter & Schmock, Uwe, 1998. "Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 233-251, September.
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