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Randomly weighted self-normalized Lévy processes

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  • Kevei, Péter
  • Mason, David M.
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    Abstract

    Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We show that all subsequential limits of this ratio at 0 (∞) are continuous for any nondegenerate F with finite expectation if and only if Vt belongs to the centered Feller class at 0 (∞). We also characterize when Ut/Vt has a non-degenerate limit distribution at 0 and ∞.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 490-522

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:490-522

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    Related research

    Keywords: Lévy process; Feller class; Self-normalization; Stable distributions;

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