On generalized multiplicative cascades

Quansheng Liu

Stochastic Processes and their Applications, 2000, vol. 86, issue 2, 263-286

Abstract: We consider a generalized Mandelbrot's martingale {Yn} and the associated Mandelbrot's measure [mu][omega] on marked trees. If the limit variable Z=lim Yn is not degenerate, we study the asymptotic behavior at infinity of its distribution; in the contrary case, we prove that there is an associated natural martingale Yn* converging to a non-negative random variable Z* with infinite mean. Both Z and Z* lead to non-trivial solution of a distributional equation which extends the notion of stable laws. Precise results are obtained about Hausdorff measures and packing measures of the support of the Mandelbrot's measure.

Keywords: Self-similar; cascades; Marked; trees; Branching; random; walk; Random; measures; Martingales; Functional; equations; Moments; Exponential; moments; Tails; Hausdorff; measure; Packing; measure (search for similar items in EconPapers)
Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (26)

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