Accession Number:

AD0656485

Title:

SOME RESULTS ON ALMOST SURE AND COMPLETE CONVERGENCE IN THE INDEPENDENT AND MARTINGALE CASES,

Descriptive Note:

Corporate Author:

PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s):

Report Date:

1967-08-01

Pagination or Media Count:

72.0

Abstract:

Let Omega,F,P be a probability space, Dsubscript n, n or 1 be a sequence of independent random variables, asubscript nk be a matrix of real numbers, Tsubscript nm Summation, k1 to km, of asubscript nk Dsubscript k, and Tsubscript n be the almost sure limit as m approaches infinity when it exists. Tsubscript n is said to converge completely to zero 15 if Summation, n1 to ninfinity, of pabsolute value of T subscript n epsilon infinity for all epsilon o. Various conditions are given for the complete or almost sure convergence of Tsubscript n to zero, extending or improving results given by others. In Chapter II, we extend to the martingale case a result of Chow concerning the complete convergence of Tsubscript n to zero where the D sub ns are generalized Gaussian. In Chapter III a number of almost sure convergence results are established in the martingale case. Chapter IV an extension of the Kolmogorov law of the iterated logarithm to the martingale case is made.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE