论文信息 - A new version of the strong law of large numbers for dependent vector processes with decreasing correlation

A new version of the strong law of large numbers for dependent vector processes with decreasing correlation

The new form of the strong law of large numbers for dependent vector sequences using the "double averaged" correlation function is presented. The suggested theorem generalizes well-known Cramer-Lidbetter's theorem (1969) and give more general conditions for fulfilling the strong law of large numbers within the class of vector random processes generated by a nonstationary stable forming filters with an absolutely integrable impulse function.

Alexander S. Poznyak | A. Poznyak

[1] P. Hall,et al. Martingale Limit Theory and its Application. , 1984 .

[2] Alexander S. Poznyak,et al. Self-Learning Control of Finite Markov Chains , 2000 .

[3] J. Neveu,et al. Mathematical foundations of the calculus of probability , 1965 .

[4] Hiroshi Takeda,et al. Learning Control of Finite Markov Chains , 1981 .

[5] A. N. Kolmogorov,et al. Foundations of the theory of probability , 1960 .

[6] P. Hall,et al. Martingale Limit Theory and Its Application , 1980 .