Randomly weighted self-normalized Lévy processes

Péter Kevei and David M. Mason

Stochastic Processes and their Applications, 2013, vol. 123, issue 2, 490-522

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 ∞.

Keywords: Lévy process; Feller class; Self-normalization; Stable distributions (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:2:p:490-522

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DOI: 10.1016/j.spa.2012.10.002

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