scholarly journals An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series

1977 ◽  
Vol 5 (5) ◽  
pp. 779-786 ◽  
Author(s):  
Jean-Pierre Gabriel
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Finite Dimensional ◽  
Convergence Of Series ◽  
Inequality For Sums

scholarly journals The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables

2010 ◽  
Vol 47 (04) ◽  
pp. 908-922 ◽  
Author(s):  
Yiqing Chen ◽  
Anyue Chen ◽  
Kai W. Ng
Keyword(s):  
Law Of Large Numbers ◽  
Large Deviation ◽  
Random Variables ◽  
Renewal Theory ◽  
Independent Random Variables ◽  
Strong Law ◽  
Finite Dimensional ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
New Inequalities

A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the same marginal distributions. The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.

Multivariate extremal processes generated by independent non-identically distributed random variables

1975 ◽  
Vol 12 (03) ◽  
pp. 477-487 ◽  
Author(s):  
Ishay Weissman
Keyword(s):  
Poisson Process ◽  
Random Variables ◽  
Independent Random Variables ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Extremal Processes

Letbe thekth largest amongXn1, …,Xn[nt], whereXni= (Xi– an)/bn, {Xi} is a sequence of independent random variables andbn> 0 andanare norming constants. Suppose that for eachconverges in distribution. Then all the finite-dimensional laws ofconverge. The limiting process is represented in terms of a non-homogeneous two-dimensional Poisson process.

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