THE LIMITING BEHAVIORS OF LINEAR RANDOM FIELDS GENERATED BY LNQD RANDOM VARIABLES ON ℤ2

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 4,  2011, pp.591-602
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.4.591
Title & Authors
THE LIMITING BEHAVIORS OF LINEAR RANDOM FIELDS GENERATED BY LNQD RANDOM VARIABLES ON ℤ2
Ko, Mi-Hwa;

Abstract
In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\small{\mathbb{Z}^2}$.
Keywords
Central limit theorem;Strong law of large numbers;Linearly negative quadrant dependence;Random fields;Linear random field;Beveridge-Nelson decomposition;
Language
English
Cited by
References
1.
Banys, P., Davydov, Y. and Paulaskas, V.(2010) Remarks on the SLLN for linear random fields, Statist. Probab. Lett. 80 489-496

2.
Billingsley, P.(1968) Convergence of Probability Measure, Wiley, New York.

3.
Esary, J., Proschan, F. and Walkup, D.(1967) Association of random variables with applications, Ann. Math. Statist. 38 1466-1474

4.
Joag-Dev, K. and Proschan, F. (1983) Negative association of random variables with applications, Ann. Statist. 11 286-295

5.
Kim, T.S., Ko, M.H. and Choi, Y.K.(2008) The invariance principle for lin- ear multi-parameter stochastic processes generated by associated fields, Statist. Probab. Lett. 78 3298-3303

6.
Ko, M.H.(2011) The strong law of large numbers for linear random fields gener- ated by negatively associated random variables on \$\mathbb{Z}^d\$, Rocky Mountain J. Math. in press.

7.
Lehmann, E.L.(1966) Some concepts of dependence, Ann. Math. Statist. 37 1137- 1153

8.
Matula, P.(1992) A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15 209-213

9.
Marinucci, M. and Poghosyan, S.(2001) Asymptotics for linear random fields, Statist. Probab. Lett. 51 131-141

10.
Newman, C.(1980) Normal uctations and the FKG inequalities, Comm. Math. Phys. 74 119-128

11.
Paulauskas, V.(2010) On Beveridge-Nelson decomposition and limit theorems for linear random field, J. Multi. Anal. 101 621-639

12.
Phillips, P.C.B. and Solo, V.(1992) Asymptotics for linear processes, Ann. Statist. 20 971-1001

13.
Zhang, L.X.(2000) A functional central limit theorem for asymptotically nega- tively associated dependent random variables, Acta. Math. Hungar. 86 237-259