# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Strong limit theorems for weighted sums of NOD sequence and exponential inequalities. (English) Zbl 1234.60035
Many of classical limit theorems for the sum of independent identically distributed (i.i.d.) random variables have been extended to weighted sums of i.i.d. random variables. This paper considers the extensions of some strong limit theorems to the weighted sum of a sequence of negatively orthant-dependent (NOD) random variables introduced by {\it K. Joag-Dev} and {\it F. Proschan} [Ann. Stat. 11, 286--295 (1983; Zbl 0508.62041)]. After establishing some basic properties of NOD random variables, the authors provide some results on the complete and almost surely convergences of the weighted sum of NOD sequences, which are generalizations of results provided by {\it R. Giuliano Antonini, J. S. Kwon, S. H. Sung} and {\it A. I. Volodin} [Stochastic Anal. Appl. 19, No. 6, 903--909 (2001; Zbl 0989.60037)] for the weighted sum of i.i.d. random variables. Finally, an exponential inequality is obtained for bounded NOD sequences, which may be useful to obtain the rate of convergence for NOD sequences, although no result in this direction is given in this paper.

##### MSC:
 60F15 Strong limit theorems 60E15 Inequalities in probability theory; stochastic orderings
Full Text: