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| LIMIT THEOREM FOR A CLASS OF SEQUENCE OFWEAKLY DEPENDENT RANDOM VARIABLES |
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Citation： |
LIN ZHENGYAN.LIMIT THEOREM FOR A CLASS OF SEQUENCE OFWEAKLY DEPENDENT RANDOM VARIABLES[J].Chinese Annals of Mathematics B,1981,2(2):181~185 |
| Page view： 822
Net amount： 727 |
Authors： |
LIN ZHENGYAN; |
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| Abstract： |
In this paper, we consider a central limit theorem for the sequence of stationary m-dependent random variables, the variance of which is possibly infinite.
Theorem. Let {Xn, n=l, 2,...} be a sequence of stationary m-dependent random variables with means zero. The following conditions are satisfied.
(i) \[{M^2}\int_{{\text{|}}{X_1}| > M} {dP} /\int_{{X_1}| < M} {X_1^2} dP \to 0{\kern 1pt} {\kern 1pt} {\kern 1pt} (M \to \infty )\]
(ii) \[\int_{\{ {X_1}| < M,|{X_i}| < M} {X_1^{}} {X_i}dP/\int_{|{X_1}| < M} {X_1^2} dP \to 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (M \to \infty )\]
then there are constants Bsubsub>0, such that \[\frac{1}{{{B_n}}}\sum\limits_{i = 1}^n {{X_1}} \] converges in distribution N(0,1). |
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