A FUNCTIONAL CENTRAL LIMIT THEOREM FOR LINEAR RANDOM FIELD GENERATED BY NEGATIVELY ASSOCIATED RANDOM FIELD

다국어 초록 (Multilingual Abstract)

We prove a functional central limit theorem for a linear random ¯eld generated by negatively associated multi-dimensional random variables. Under a ¯nite second moment condition we ex- tend the result in Kim, Ko and Choi[Kim,T.S, Ko,M.H and Choi, Y.K.,2008. The invariance principle for linear multi-parameter sto-chastic processes generated by associated ¯elds. Statist. Probab. Lett. 78, 3298-3303] to the negatively associated case.

참고문헌 (Reference)

1 M. L. Straf, "Weak convergence of stochastic processes with several parame- ters" 187-221, 1970

2 C. Su, "The moment inequalities and weak conver- gence for negatively associated sequences" 40A : 172-182, 1997

3 T. S. Kim, "The invariance principle for linear multi- parameter stochastic processes generated by associated ¯elds" 78 : 3298-3303, 2008

4 K. Joag-Dev, "Negative association of random variables with applications" 11 : 286-295, 1983

5 S. Poghosyan, "Invariance principle for martingale-di®erence ran- dom ¯elds" 38 : 235-245, 1998

6 P. Billingsley, "Convergence of Probability Measures" Wiley 1968

7 M. Marinucci, "Asymptotics for linear random ¯elds" 51 : 131-141, 2001

8 P. C. B. Phillips, "Asymptotics for linear processes" 20 : 971-1001, 1992

9 C. G. Roussas, "Asymptotic normality of random ¯elds of positively or negatively associated processes" 50 : 152-173, 1994

10 C. M. Newman, "Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Inequalities in Probability and Statistics, Tong, Y.L., ed." IMS Lecture-Notes-Monograph Series 127-140, 1984

11 P. Matula, "A note on the almost sure convergence of sums of negatively depen- dent random variables" 15 : 209-213, 1992

12 L. X. Zhang, "A functional central limit theorem for asymptotically negatively dependent random variables" 86 : 237-259, 2000