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Strong and conditional invariance principles for samples attracted to stable laws |
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| Authors: | Raoul LePage Krzysztof Podgórski Michał Ryznar |
| Affiliation: | (1) Department of Probability and Statistics, Michigan State University, East Lansing, MI 48823, USA. E-mail: entropy@msu.edu, US;(2) Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202-3216, USA. E-mail: kpodgorski@math.iupui.edu, IN;(3) Institute of Mathematics, Technical University of Wroclaw, 50-370 Wroclaw, POLAND E-mail: ryznar@graf.im.pwr.wroc.p1, PL |
| Abstract: | Summary. We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations. Received: 11 April 1994 / In revised form: 5 November 1996 |
| Keywords: | Mathematics Subject Classification (1991): 60E07 60F17 Secondary 60F15 60G50 |
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