### Abstract

1. Let Xl, X2,…, Xn… be independent random variables and let Sn = Formula Presented. In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of Sn as n → ∞ is considered and its true order of magnitude is found with probability one. A counterpart to that problem is to consider the lower limit of Sn as n → ∞ and to make a statement about its order of magnitude with probability one.

Original language | English |
---|---|

Title of host publication | Selected Works of Kai Lai Chung |

Publisher | World Scientific Publishing Co. |

Pages | 75-85 |

Number of pages | 11 |

ISBN (Electronic) | 9789812833860 |

ISBN (Print) | 9789812833853 |

DOIs | |

Publication status | Published - Jan 1 2008 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Selected Works of Kai Lai Chung*(pp. 75-85). World Scientific Publishing Co.. https://doi.org/10.1142/9789812833860_0007

**On the lower limit of sums of independent random variables.** / Chung, Kai Lai; Erdős, P.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Selected Works of Kai Lai Chung.*World Scientific Publishing Co., pp. 75-85. https://doi.org/10.1142/9789812833860_0007

}

TY - CHAP

T1 - On the lower limit of sums of independent random variables

AU - Chung, Kai Lai

AU - Erdős, P.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 1. Let Xl, X2,…, Xn… be independent random variables and let Sn = Formula Presented. In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of Sn as n → ∞ is considered and its true order of magnitude is found with probability one. A counterpart to that problem is to consider the lower limit of Sn as n → ∞ and to make a statement about its order of magnitude with probability one.

AB - 1. Let Xl, X2,…, Xn… be independent random variables and let Sn = Formula Presented. In the so-called law of the iterated logarithm, completely solved by Feller recently, the upper limit of Sn as n → ∞ is considered and its true order of magnitude is found with probability one. A counterpart to that problem is to consider the lower limit of Sn as n → ∞ and to make a statement about its order of magnitude with probability one.

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UR - http://www.scopus.com/inward/citedby.url?scp=84973452370&partnerID=8YFLogxK

U2 - 10.1142/9789812833860_0007

DO - 10.1142/9789812833860_0007

M3 - Chapter

SN - 9789812833853

SP - 75

EP - 85

BT - Selected Works of Kai Lai Chung

PB - World Scientific Publishing Co.

ER -