Abstract
Let X 1, X 2,... be independent, but not necessarily identically distributed random variables in the domain of attraction of a normal law or a stable law with index 0 < α < 2. Using suitable self-normalizing (or Studentizing) factors, laws of the iterated logarithm for self-normalized Hanson–Russo type increments are discussed. Also, some analogous results for self-normalized weighted sums of i.i.d. random variables are given.
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Liang, HY., Steinebach, J.G. Self-Normalized LIL for Hanson–Russo Type Increments. J Theor Probab 19, 70–88 (2006). https://doi.org/10.1007/s10959-006-0011-8
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DOI: https://doi.org/10.1007/s10959-006-0011-8