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.
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Received: 11 April 1994 / In revised form: 5 November 1996
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LePage, R., Podgórski, K. & Ryznar, M. Strong and conditional invariance principles for samples attracted to stable laws. Probab Theory Relat Fields 108, 281–298 (1997). https://doi.org/10.1007/s004400050110
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DOI: https://doi.org/10.1007/s004400050110