| 徐业基.具有离散参数齐次随机场的线性预测与马氏性(II)[J].数学研究及应用,2006,26(4):785~794 |
| 具有离散参数齐次随机场的线性预测与马氏性(II) |
| Linear Prediction Theory and Markov Models of a Homogeneous Random Field with Discrete Parameters (II) |
| 投稿时间：2004-02-16 |
| DOI：10.3770/j.issn:1000-341X.2006.04.019 |
| 中文关键词: 线性预测 预测值 预测误差 马氏性. |
| 英文关键词:linear prediction predictor predictor error Markov property. |
| 基金项目: |
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| 中文摘要: |
| 本文提出和研究3个新型的具有离散参数齐次随机场$\{x(m,n)\}$的马氏性问题,求出了它们具有马氏性的充分必要条件. |
| 英文摘要: |
| Generally, the definations of the Markov type for homogeneous random field as follows: Let $H_X(T)$ be the closed linear manifold spanned by all $X(m,n), (m,n)\in T, T_0\subset T$. $(m',n')\bar{\in}T$, if $P_{H_X(T)}X(m',n')=P_{H_X(T_0)}X(m',n')$, then we say that $H_X(T)$ has the Morkov property for $H_X(T_0)$ at $X(m',n')$. In this paper, three types are posed and discussed: 1). $T = \{(m,n), -\infty
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