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 Electronic Communications in Probability > Vol. 7 (2002) > Paper 5 open journal systems 


Asymptotics for Products of Sums and U-statistics

Grzegorz Rempala, University of Louisville
Jacek Wesolowski, Politechnika Warszawska


Abstract
The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to non-degenerate U-statistics.


Full text: PDF

Pages: 47-54

Published on: January 20, 2002
Bibliography
  1. Arnold, B.C., Villasenor, J.A. (1998) The asymptotic distribution of sums of records.Extremes 1:3, 351-363. Math. Review 02a:6002
  2. Hoeffding, W. (1948).A class of statistics with asymptotically normal distribution. Ann. Math. Statistics, 19:293-325. Math. Review 10,134g
  3. Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley & Sons Inc., New York. Math. Review  82a:62003
  4. Resnick, S.I. (1973)  Limit laws for record values. Stochastic Processes and Their Applications 1, 67-82. Math. Review  50 #14895













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Electronic Communications in Probability. ISSN: 1083-589X