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| WEAK CONVERGENCE FOR NON-UNIFORM φ-MIXING RANDOM FIELDS |
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Citation： |
Lu Chuanrong.WEAK CONVERGENCE FOR NON-UNIFORM φ-MIXING RANDOM FIELDS[J].Chinese Annals of Mathematics B,1997,18(1):71~78 |
| Page view： 1015
Net amount： 722 |
Authors： |
Lu Chuanrong; |
Foundation： |
Project supported by the National Natural Science
Foundation of China and Natural Science Fund of Zhejiang Province |
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| Abstract： |
Let $\{\xi_{\bold t}, {\bold t}
\in {\bold Z}^d\}$ be a nonuniform $\varphi$-mixing strictly stationary
real random field with
$E\xi_{\bold 0}=0, E|\xi_{\bold 0}|^{2+\delta}<\infty$ for some
$0<\delta<1$. A sufficient
condition is given for the sequence of partial sum set-indexed process
$\{Z_n(A),\ A\in \Cal A\}$ to converge to Brownian motion. By a direct
calculation, the author shows
that the result holds for a more general class of set index ${\Cal A}$, where
${\Cal A}$ is assumed only to have the metric entropy exponent $r, 0 |
Keywords： |
Weak convergence of partial-sum processes, Set-indexed process,
Nonuniform $\varphi$-mixing, Random fields |
Classification： |
60F17, 60B10, 60K35 |
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