On a non-linear prediction problem for one-dimensional stochastic processes
On a non-linear prediction problem for one-dimensional stochastic processes
复制标题
一维随机过程的非线性预测问题
DOI：
10.4099/math1924.27.51
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Y. Okabe
中科院分区：
文献类型：
--
作者：
M. Matsuura;Y. Okabe
在非线性预报器中，我们指的是未来随机变量X(n+p)的条件期望E(X(n+p)|Bn0(X))，其中Din m(X)表示所有随机变量X(K)(-oo<；k<；n)关于其可测的最小ƒ-域。将每个随机变量X(N)(n·̧Z)看作实希尔伯特空间L2(ƒ？，B，P)的一个元素，我们发现非线性预测器与向量Pnn(X)X(n+p)一致，其中Pnn(X)表示从L2(ƒ？，B，P)到闭子空间Nn(X)EL2(i，Bn0(X)，P)的投影算子.与条件(B)一起，Masani和Wiener首先使用Stone-Weerstrass的
By the non-linear predictor, we mean the conditional expectation E(X(n+p)| Bn 0(X)) of the future random variable X(n+p) conditioned by the past sub ƒÐfield B,0(X)(n E Z, p E N), where din m(X) stands for the smallest ƒÐ-field with respect to which all random variables X(k)(-oo<k<n) are measur able. By regarding each random variable X(n)(n• ̧Z) as an element of the real Hilbert space L2(ƒ¶, B, P), we find that the non-linear predictor agrees with the vector PNn(X)X(n+p), where PNn(X) stands for the projection operator from L2(ƒ¶, B, P) onto the closed subspace Nn(X)eL2(i, Bn0(X),P). Together with condition (B), Masani and Wiener first use Stone-Weierstrass's