DOI QR코드

DOI QR Code

WEAK LAW OF LARGE NUMBERS FOR ADAPTED DOUBLE ARRAYS OF RANDOM VARIABLES

  • Published : 2008.05.31

Abstract

The aim of this paper is to extend the "classical degenerate convergence criterion" and the Feller weak law of large numbers to double adapted arrays of random variables.

Keywords

References

  1. A. Adler, A. Rosalsky, and A. I. Volodin, A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett. 32 (1997), no. 2, 167-174 https://doi.org/10.1016/S0167-7152(97)85593-9
  2. S. E. Ahmed, S. H. Sung, and A. I. Volodin, Mean convergence theorem for arrays of random elements in martingale type p Banach spaces, Bull. Inst. Math. Acad. Sinica 30 (2002), no. 2, 89-95
  3. Y. S. Chow and H. Teicher, Probability Theory, Independence, interchangeability, martingales. Springer-Verlag, New York-Heidelberg, 1978
  4. A. Gut, An extension of Feller's weak law of large numbers, http://www.math.uu.se/research/pub/Gut8.pdf
  5. D. H. Hong and S. Lee, A general weak law of large numbers for arrays, Bull. Inst. Math. Acad. Sinica 24 (1996), no. 3, 205-209
  6. D. H. Hong and K. S. Oh, On the weak law of large numbers for arrays, Statist. Probab. Lett. 22 (1995), no. 1, 55-57 https://doi.org/10.1016/0167-7152(94)00047-C
  7. D. H. Hong, M. Ordonez Cabrera, S. H. Sung, and A. I. Volodin, On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett. 46 (2000), no. 2, 177-185 https://doi.org/10.1016/S0167-7152(99)00103-0
  8. D. H. Hong and A. I. Volodin, Marcinkiewicz-type law of large numbers for double arrays, J. Korean Math. Soc. 36 (1999), no. 6, 1133-1143
  9. P. Hall and C. C. Heyde, Martingale Limit Theory and Its Application, Probability and Mathematical Statistics. Academic Press, Inc. Harcourt Brace Jovanovich, Publishers, New York-London, 1980
  10. M. Loeve, Probability Theory. I, Fourth edition. Graduate Texts in Mathematics, Vol. 45. Springer-Verlag, New York-Heidelberg, 1977
  11. S. H. Sung, Weak law of large numbers for arrays, Statist. Probab. Lett. 38 (1998), no. 2, 101-105 https://doi.org/10.1016/S0167-7152(97)00159-4
  12. S. H. Sung, T. C. Hu, and A. I. Volodin, On the weak laws for arrays of random variables, Statist. Probab. Lett. 72 (2005), no. 4, 291-298 https://doi.org/10.1016/j.spl.2004.12.019
  13. S. H. Sung, On the weak laws with random indices for partial sums for arrays of random elements in martingale type p Banach spaces, Bull. Korean Math. Soc. 43 (2006), no. 3, 543-549 https://doi.org/10.4134/BKMS.2006.43.3.543

Cited by

  1. The degenerate convergence criterion and Feller’s weak law of large numbers for double arrays in noncommutative probability vol.83, pp.7, 2013, https://doi.org/10.1016/j.spl.2013.04.003
  2. On the weak law of large numbers for double adapted arrays of random elements in p-uniformly smooth Banach space vol.30, pp.2, 2009, https://doi.org/10.1134/S1995080209020097
  3. A characterization of p-uniformly smooth Banach spaces and weak laws of large numbers for d-dimensional adapted arrays vol.72, pp.2, 2010, https://doi.org/10.1007/s13171-010-0020-7