Equation Chapter 1 Section 1 Concentration Inequality for m-dependent Random Vectors in Hilbert Spaces
Main Article Content
Abstract
Let be a sequence of -dependent random vectors taking values in a real separable Hilbert space. In this work we introduce concentration inequality for the partial sums of . Then, we give the weak laws of large numbers for weighted sums of .
Keywords:
Hilbert spaces, m-dependent, concentration inequalities.*
References
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[3] N. T. T. Hien, L. V.Thanh, On the Weak Laws of Large Numbers for Sums of Negatively Associated Random Vectors in Hilbert Spaces, Statistics and Probability Letters, Vol. 107, 2015, pp. 236-245, https://doi.org/10.1016/j.spl.2015.08.030.
[4] L. V. Dung, T. C. Son, T. M. Cuong, Weak Laws of Large Numbers for Weighted Coordinatewise Pairwise NQD Random Vectors in Hilbert Spaces, Journal of the Korean Mathematical Society, Vol. 56, No. 1, 2019,
pp. 457-473, https://doi.org/10.4134/JKMS.j180217.
[5] B. K. Hang, T. M. Cuong, T. C. Son, Weak Laws of Large Numbers for Negatively Superadditive Dependent Random Vectors in Hilbert Spaces, VNU Journal of Science Mathematics, Vol. 37, No. 2, 2021, pp. 84-92, https://doi.org/10.25073/2588-1124/vnumap.4571.
[6] T. C. Son, T. M. Cuong, L. V. Dung, On the Almost Sure Convergence for Sums of Negatively Superadditive Dependent Random Vectors in Hilbert Spaces And Its Application, Communications in Statistics - Theory and Methods, Vol. 49, No. 11, 2019, pp. 2770--2786, https://doi.org/10.1080/03610926.2019.1584304.
[2] F. Chung, L. Lu, Concentration Inequalities and Martingale Inequalities: A Survey, {Internet Math}, Vol. 3,
No. 1, 2006, pp. 79-127, https://doi.org/10.1080/15427951.2006.10129115.
[3] N. T. T. Hien, L. V.Thanh, On the Weak Laws of Large Numbers for Sums of Negatively Associated Random Vectors in Hilbert Spaces, Statistics and Probability Letters, Vol. 107, 2015, pp. 236-245, https://doi.org/10.1016/j.spl.2015.08.030.
[4] L. V. Dung, T. C. Son, T. M. Cuong, Weak Laws of Large Numbers for Weighted Coordinatewise Pairwise NQD Random Vectors in Hilbert Spaces, Journal of the Korean Mathematical Society, Vol. 56, No. 1, 2019,
pp. 457-473, https://doi.org/10.4134/JKMS.j180217.
[5] B. K. Hang, T. M. Cuong, T. C. Son, Weak Laws of Large Numbers for Negatively Superadditive Dependent Random Vectors in Hilbert Spaces, VNU Journal of Science Mathematics, Vol. 37, No. 2, 2021, pp. 84-92, https://doi.org/10.25073/2588-1124/vnumap.4571.
[6] T. C. Son, T. M. Cuong, L. V. Dung, On the Almost Sure Convergence for Sums of Negatively Superadditive Dependent Random Vectors in Hilbert Spaces And Its Application, Communications in Statistics - Theory and Methods, Vol. 49, No. 11, 2019, pp. 2770--2786, https://doi.org/10.1080/03610926.2019.1584304.