JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ALMOST SURE MARCINKIEWICZ TYPE RESULT FOR THE ASYMPTOTICALLY NEGATIVELY DEPENDENT RANDOM FIELDS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 31, Issue 4,  2009, pp.505-513
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2009.31.4.505
 Title & Authors
ALMOST SURE MARCINKIEWICZ TYPE RESULT FOR THE ASYMPTOTICALLY NEGATIVELY DEPENDENT RANDOM FIELDS
Kim, Hyun-Chull;
  PDF(new window)
 Abstract
Let {} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for > 1 and > < if and only if ( > ) < for all > 0, where logx = max{1,log x}.
 Keywords
asymptotically linear negative quadrant dependence;random field;identically distributed;complete convergence;maximal moment inequality;
 Language
English
 Cited by
 References
1.
Gut, A.(1978) Marcinkiewicz and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6 467-482 crossref(new window)

2.
Joag-Dev, K. and Proschan, F.(1983) Negative association of random variables with applications, Ann. Math. Statist. 11 286-295 crossref(new window)

3.
Peligrad, M. and Gut, A.(1999) Almost sure results for a class of dependent random variables, J. Theor. Probab. 12 87-104 crossref(new window)

4.
Zhang L. X.(2000) A functional central limit theorem for asymptotically negatively dependent random fields, Acta Math. Hungar. 86 237-259 crossref(new window)

5.
Lehmann(1966) Some concepts of dependence, Ann. Math. Stat. 37 1137-1153 crossref(new window)

6.
Newman, C.M.(1984) Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Inequalities in Statistics and Probability(Tong, Y.L. ed, IMS, Hayward, CA, 1984) Vol. 5 pp. 127-140