scholarly journals AN ALMOST SURE CONVERGENCE THEOREM IN A STOCHASTIC APPROXIMATION METHOD WITH DEPENDENT RANDOM VARIABLES

10.5109/13134 ◽  
1979 ◽  
Vol 18 (3/4) ◽  
pp. 95-112
Author(s):  
Masafumi Watanabe
Keyword(s):  
Stochastic Approximation ◽  
Approximation Method ◽  
Convergence Theorem ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Dependent Random Variables

scholarly journals Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Ruixue Wang ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables

In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space.

SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES

2016 ◽  
Vol 32 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Convergence Theorem ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Independent Random Variables ◽  
Strong Law ◽  
Limiting Behavior ◽  
Associated Random Variables ◽  
Large Numbers

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

scholarly journals On exact strong laws of large numbers under general dependence conditions

2018 ◽  
Vol 38 (1) ◽  
pp. 103-121 ◽  
Author(s):  
André Adler ◽  
Przemysław Matuła
Keyword(s):  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Laws Of Large Numbers ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Strong Laws ◽  
Large Numbers ◽  
Dependence Conditions

We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.

Sign in / Sign up

Export Citation Format

Share Document