Strong Limit Theorems for Dependent Random Variables
In This Article We establish moment inequality of
dependent random variables,furthermore some theorems of strong law
of large numbers and complete convergence for sequences of dependent
random variables. In particular, independent and identically
distributed Marcinkiewicz Law of large numbers are generalized to
the case of m0-dependent sequences.
[1] Fazekas, I., Klesov, O., 2000. A general approach to the strong law of
large numbers. Theory Probab. Appl. 45, 436-449.
[2] Fikhtengolts, G.M., 1954. A Course of Differential and Integral Calculus.
People-s Education Press, Beijing (in Chinese).
[3] Hu Shuhe,2005. A general approach rate to the strong law of large
numbers.Statistics & Probability Letters 76,843-851
[4] Shao, Q., 2000. A comparison theorem on maximal inequalities between
negatively associated and independent random variables.J. Theoret.
Probab. 13 (2), 343-356.
[5] Shao, Q., Yu, H., 1996. Weak convergence for weighed empirical processes
of dependent sequences. Ann. Probab. 24, 2098-2127.
[6] Yang, S., 2000. Moment inequalities for partial sums of random variables.
Sci. China (series A, Chinese) 30 (3), 218-223.
[7] Yang, S., 2001. Moment inequalities for partial sums of random variables.
Sci. China (series A, English) 44, 1-6.
[8] Ryozo, Y.,1980. Moment Bounds for Stationary Mixing Sequences,Z. W.
verw. Gebiete 52, 45-57.
[1] Fazekas, I., Klesov, O., 2000. A general approach to the strong law of
large numbers. Theory Probab. Appl. 45, 436-449.
[2] Fikhtengolts, G.M., 1954. A Course of Differential and Integral Calculus.
People-s Education Press, Beijing (in Chinese).
[3] Hu Shuhe,2005. A general approach rate to the strong law of large
numbers.Statistics & Probability Letters 76,843-851
[4] Shao, Q., 2000. A comparison theorem on maximal inequalities between
negatively associated and independent random variables.J. Theoret.
Probab. 13 (2), 343-356.
[5] Shao, Q., Yu, H., 1996. Weak convergence for weighed empirical processes
of dependent sequences. Ann. Probab. 24, 2098-2127.
[6] Yang, S., 2000. Moment inequalities for partial sums of random variables.
Sci. China (series A, Chinese) 30 (3), 218-223.
[7] Yang, S., 2001. Moment inequalities for partial sums of random variables.
Sci. China (series A, English) 44, 1-6.
[8] Ryozo, Y.,1980. Moment Bounds for Stationary Mixing Sequences,Z. W.
verw. Gebiete 52, 45-57.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50031", author = "Libin Wu and Bainian Li", title = "Strong Limit Theorems for Dependent Random Variables", abstract = "In This Article We establish moment inequality of
dependent random variables,furthermore some theorems of strong law
of large numbers and complete convergence for sequences of dependent
random variables. In particular, independent and identically
distributed Marcinkiewicz Law of large numbers are generalized to
the case of m0-dependent sequences.", keywords = "Lacunary System, Generalized Gaussian, NA sequences, strong law of large numbers.", volume = "5", number = "4", pages = "518-3", }