具有线性回归的广义平稳随机场--算子方法
Generalized stationary random fields with linear regressions - an operator approach
摘要：
研究了满足\[ \wwo{X_k}{...,X_{k-2},X_{k-1},X_{k+1},X_{k+2},...}=\sum_{j=1}^\infty b_j(X_{k-j}+X_{k+j}) \]的平方可积〔的〕随机序列$\mathbf{X}=(X_{k})_{k\in\mathbb{Z}}$对实数序列$(b_n)_{n\in\nat}$的条件期望$\wwo{X_k}{...,X_{k-2},X_{k-1}}$的存在性、$L^2$ -平稳性和线性性.分析依赖于Laurent和Toeplitz算子技术的使用。
英文摘要：
Existence, $L^2$-stationarity and linearity of conditional expectations $\wwo{X_k}{...,X_{k-2},X_{k-1}}$ of square integrable random sequences $\mathbf{X}=(X_{k})_{k\in\mathbb{Z}}$ satisfying \[ \wwo{X_k}{...,X_{k-2},X_{k-1},X_{k+1},X_{k+2},...}=\sum_{j=1}^\infty b_j(X_{k-j}+X_{k+j}) \] for a real sequence $(b_n)_{n\in\nat}$, is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
