Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 12 (2007) > Paper 42 open journal systems 


On the strong law of large numbers for d-dimensional arrays of random variables

Thanh Le Van, Vinh University


Abstract
In this paper, we provide a necessary and sufficient condition for general d-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some strong laws of large numbers for d-dimensional arrays of blockwise independent and blockwise orthogonal random variables.


Full text: PDF

Pages: 434-441

Published on: November 21, 2007
Bibliography
  1. Chobanyan, S., Levental, S., and Mandrekar, V. Prokhorov blocks and strong law of large numbers under rearrangements. J. Theoret. Probab. 17 (2004), 647-672. MR2091554
  2. Chow, Y. S. and Teicher, H. Probability Theory: Independence, Interchangeability, Martingales, 3rd Ed. Springer-Verlag, New York, 1997. MR1476912
  3. Chung, K. L. Note on some strong laws of large numbers. Amer. J. Math. 69 (1947), 189-192. MR0019853
  4. Gaposhkin, V.F. On the strong law of large numbers for blockwise independent and blockwise orthogonal random variables. Teor. Veroyatnost. i Primenen. 39 (1994), 804-812 (in Russian). English translation in Theory Probab. Appl. 39 (1994), 667-684 (1995). MR1347654
  5. Gut, A. Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices. Ann. Probab. 6 (1978), 469-482. MR0494431
  6. Mikosch, T. and Norvaisa, R. Strong laws of large numbers for fields of Banach space valued random variables. Probab. Th. Rel. Fields. 74 (1987), 241-253. MR0871253
  7. Moricz, F. Moment inequalities for the maximum of partial sums of random fields. Acta Sci. Math. 39 (1977), 353-366. MR0458535
  8. Moricz, F. Strong limit theorems for quasi-orthogonal random fields. J. Multivariate. Anal. 30 (1989), 255-278. MR1015372
  9. Moricz, F. Strong limit theorems for blockwise m-dependent and blockwise quasiorthogonal sequences of random variables. Proc. Amer. Math. Soc. 101 (1987), 709-715. MR0911038
  10. Smythe, R.T. Strong laws of large numbers for r-dimensional arrays of random variables. Ann. Probab. 1 (1973), 164-170. MR0346881
  11. Thanh. L. V. Mean convergence theorems and weak laws of large numbers for double arrays of random variables. J. Appl. Math. Stochastic Anal. 2006, Art. ID 49561, 1 - 15.















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X