Some Strong Laws for Normed Weighted Sums of Stochastically Dominated Banach Space Valued Random Elements Irrespective of Their Joint Distributions

References

• Adler , A. , and Rosalsky , A. 1987 . Some general strong laws for weighted sums of stochastically dominated random variables . Stochastic Analysis and Applications 5 : 1 – 16 .
   Web of Science ®Google Scholar
• Adler , A. , Rosalsky , A. , and Taylor , R.L. 1989 . Strong laws of large numbers for weighted sums of random elements in normed linear spaces . International Journal of Mathematics and Mathematical Sciences 12 : 507 – 530 .
   Google Scholar
• Adler , A. , Rosalsky , A. , and Taylor , R.L. 1992. Some strong laws of large numbers for sums of random elements. Bulletin of the Institute of Mathematics Academia Sinica 20:335–357.
   Google Scholar
• Feller , W. 1971 . An Introduction to Probability Theory and Its Applications. Vol. II. , 2nd ed. , John Wiley , New York .
   Google Scholar
• Knopp , K. 1951 . Theory and Application of Infinite Series. , 2nd English ed. , Blackie and Son , London .
   Google Scholar
• Petrov , V.V. 1973 . The order of growth of sums of dependent random variables . Teoriya Veroyatnosteĭ i ee Primeneniya 18:358–361 (in Russian). English translation in Theory Probability and its Applications 18 : 348 – 350 .
   Google Scholar
• Rosalsky , A. , and Stoica , G. 2010 . On the strong law of large numbers for identically distributed random variables irrespective of their joint distributions . Statistics and Probability Letters 80 : 1265 – 1270 .
   Google Scholar
• Sung , S.H. 1997 . Almost sure convergence for weighted sums of i.i.d. random variables . Journal of the Korean Mathematical Society 34 : 57 – 67 .
   Google Scholar
• Taylor , R.L. 1978 . Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces . Lecture Notes in Mathematics, No. 672 , Springer-Verlag , Berlin .
   Google Scholar
• Teicher , H. 1985 . Almost certain convergence in double arrays . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 69 : 331 – 345 .
   Web of Science ®Google Scholar
• Wei , D. , and Taylor , R.L. 1978 . Convergence of weighted sums of tight random elements . Journal of Multivariate Analysis 8 : 282 – 294 .
   Web of Science ®Google Scholar