scholarly journals On the strong law of large numbers for weighted sums of φ-mixing random variables

2014 ◽  
pp. 465-473 ◽  
Author(s):  
Haiwu Huang ◽  
Dingcheng Wang ◽  
Jiangyan Peng
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables

scholarly journals Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums ofρ~-Mixing Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongfeng Lan
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Sufficient And Necessary Conditions ◽  
Complete Convergence Theorem ◽  
Mixing Random Variables ◽  
Equivalent Conditions

The equivalent conditions of complete convergence are established for weighted sums ofρ~-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence ofρ~-mixing random variables is obtained.

scholarly journals On Complete Convergence for Weighted Sums ofρ*-Mixing Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Aiting Shen ◽  
Xinghui Wang ◽  
Huayan Zhu
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables ◽  
Independent And Identically Distributed

We prove the strong law of large numbers for weighted sums∑i=1n‍aniXi, which generalizes and improves the corresponding one for independent and identically distributed random variables andφ-mixing random variables. In addition, we present some results on complete convergence for weighted sums ofρ*-mixing random variables under some suitable conditions, which generalize the corresponding ones for independent random variables.

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.

REFINEMENT OF CONVERGENCE RATES FOR WEIGHTED SUMS OF INDEPENDENT RANDOM VARIABLES

2012 ◽  
Vol 05 (01) ◽  
pp. 1250007
Author(s):  
Si-Li Niu ◽  
Jong-Il Baek
Keyword(s):  
Law Of Large Numbers ◽  
Convergence Rates ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Counting Processes ◽  
Precise Asymptotics ◽  
Strong Law ◽  
Large Numbers ◽  
Passage Times

In this paper, we establish one general result on precise asymptotics of weighted sums for i.i.d. random variables. As a corollary, we have the results of Lanzinger and Stadtmüller [Refined Baum–Katz laws for weighted sums of iid random variables, Statist. Probab. Lett. 69 (2004) 357–368], Gut and Spătaru [Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000) 1870–1883; Precise asymptotics in the Baum–Katz and Davis laws of large numbers, J. Math. Anal. Appl. 248 (2000) 233–246], Gut and Steinebach [Convergence rates and precise asymptotics for renewal counting processes and some first passage times, Fields Inst. Comm. 44 (2004) 205–227] and Heyde [A supplement to the strong law of large numbers, J. Appl. Probab. 12 (1975) 173–175]. Meanwhile, we provide an answer for the possible conclusion pointed out by Lanzinger and Stadtmüller [Refined Baum–Katz laws for weighted sums of iid random variables, Statist. Probab. Lett. 69 (2004) 357–368].

scholarly journals A Strong Law of Large Numbers for Weighted Sums of i.i.d. Random Variables under Capacities

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Defei Zhang ◽  
Ping He
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Independent Identically Distributed

With the notion of independent identically distributed (i.i.d.) random variables under sublinear expectations initiated by Peng, a strong law of large numbers for weighted sums of i.i.d. random variables under capacities induced by sublinear expectations is obtained.

scholarly journals A Note on the Strong Law of Large Numbers for Arrays of Rowwiseρ˜-Mixing Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Aiting Shen ◽  
Shuhe Hu
Keyword(s):  
Law Of Large Numbers ◽  
Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Random Variables

Let{Xni,i≥1,n≥1}be an array of rowwiseρ˜-mixing random variables. Some strong law of large numbers for arrays of rowwiseρ˜-mixing random variables is studied under some simple and weak conditions.

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