Randomly weighted self-normalized Lévy processes |
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Authors: | Péter Kevei David M Mason |
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Institution: | 1. Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary;2. CIMAT, Callejón Jalisco S/N, Mineral de Valenciana, Guanajuato 36240, Mexico;3. Statistics Program, University of Delaware, 213 Townsend Hall, Newark, DE 19716, USA |
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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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Keywords: | 60G51 60F05 |
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