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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 244, Pages 73–95 (Mi znsl513)  
On the functional law of the iterated logarithm for partially observed sums of random variables

N. L. Gorna, M. A. Lifshitsb

a Friedrich-Schiller-University
b Vocational Renewal Centre Management and Computer Technologies
Full-text PDF (271 kB)
Abstract: We consider partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming that this process is available for observations 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 condition of V. A. Egorov holds, we show that FLIL is valid, while under other conditions sufficient for usual law of the iterated logarithm FLIL may fail.
Received: 08.02.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 99, Issue 2, Pages 1061–1074
DOI: https://doi.org/10.1007/BF02673627
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: N. L. Gorn, M. A. Lifshits, “On the functional law of the iterated logarithm for partially observed sums of random variables”, Probability and statistics. Part 2, Zap. Nauchn. Sem. POMI, 244, POMI, St. Petersburg, 1997, 73–95; J. Math. Sci. (New York), 99:2 (2000), 1061–1074
Citation in format AMSBIB
\Bibitem{GorLif97}
\by N.~L.~Gorn, M.~A.~Lifshits
\paper On the functional law of the iterated logarithm for partially observed sums of random variables
\inbook Probability and statistics. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 244
\pages 73--95
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl513}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1700381}
\zmath{https://zbmath.org/?q=an:0967.60039}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 99
\issue 2
\pages 1061--1074
\crossref{https://doi.org/10.1007/BF02673627}
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