Asymptotic expansions for large deviation probabilities in the strong law of large numbers

1989 ◽  
Vol 81 (2) ◽  
pp. 213-233 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Asymptotic Expansions ◽  
Law Of Large Numbers ◽  
Large Deviation ◽  
Strong Law ◽  
Large Numbers ◽  
Large Deviation Probabilities

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.

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

2010 ◽  
Vol 47 (4) ◽  
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.

scholarly journals Limit theorems for pure death processes coming down from infinity

2017 ◽  
Vol 54 (3) ◽  
pp. 720-731 ◽  
Author(s):  
Serik Sagitov ◽  
Thibaut France
Keyword(s):  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Large Deviation ◽  
Natural Generalization ◽  
Death Process ◽  
Strong Law ◽  
Large Numbers ◽  
Large Deviation Theorem

Abstract In this paper we treat a pure death process coming down from infinity as a natural generalization of the death process associated with the Kingman coalescent. We establish a number of limit theorems including a strong law of large numbers and a large deviation theorem.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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