On the functional law of the iterated logarithm for partially observed sums of random variables

N. L. Gorn, M. A. Lifshits

Research output

Abstract

We consider a partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming that this process is available for observation along an arbitrary time sequence, we fill the gaps by linear interpolation and prove the functional law of the iterated logarithm (FLIL) for sample paths obtained in this way. Assuming that the V. A. Egorov condition holds, we show that FLIL is valid, while under other conditions sufficient for the usual law of the iterated logarithm FLIL may fail.

Original languageEnglish
Pages (from-to)1061-1074
Number of pages14
JournalJournal of Mathematical Sciences
Volume99
Issue number2
DOIs
Publication statusPublished - 1 Jan 2000

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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