Convergence rates of the strong law for stationary mixing sequences

1985 ◽  
Vol 70 (2) ◽  
pp. 307-314 ◽  
Author(s):  
Magda Peligrad
Keyword(s):  
Convergence Rates ◽  
Strong Law ◽  
Mixing Sequences

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 Strong law of large numbers forρ*-mixing sequences with different distributions

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
Guang-Hui Cai
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Large Numbers ◽  
Mixing Sequences

Strong law of large numbers and complete convergence forρ*-mixing sequences with different distributions are investigated. The results obtained improve the relevant results by Utev and Peligrad (2003).

scholarly journals Laws of large numbers for infinite means with mixing sequences

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 783-793
Author(s):  
Jian Han ◽  
Xiaoqin Li ◽  
Yudan Cheng
Keyword(s):  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Mixing Sequences

In this paper, we consider the laws of large numbers with infinite means based on ?-mixing sequences. An exact weak law and a strong law are obtained for ?-mixing asymmetrical Cauchy random variables. It is also presented that the weak law cannot extend to a strong law. In addition, some simulations are presented to illustrate our results of the laws of large numbers.

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