四重马氏平稳过程的非线性预测问题

假设{X（t），t∈R^1}是由广义Wiener随机积分所定义的四重马氏平稳过程．如果该随机过程{X（t），t∈R^1}被一有界Borel可测函数f（＊）变换，则得到新的随机过程，记为Y（t）=f（X（t））．作者在本文中，首先粗略地研讨了四重马氏平稳过程{X（t），t∈R^1}及其均方导数的一些概率性质．其次，对于一些构造较简单的Borel可测函数f（＊），较详细地探讨了随机过程{Y（t）=f（X（t））}的非线性均方预测问题．

Non-lineav Prediction Pnoblems of the Quadruple Markov Stationary Processes

Let {X(t),t∈R1} be a quadruple Markov stationary process which is defined by a generalized Wiener integral. If the stochastic process {X(t),t∈R1} is transformed by a bounded Borel measurable function f(·), then we will obtain a new stochastic process which denotes by Y(t), namelyY(t)=f(X(t)). In this paper, at first the authors roughly discussed some probabilistic properties of the quadruple Markov stationary process {X(t),t∈R1} and so forth. Moreover, the authors discussed particulary the non-linear mean-square predictors of the stochastic processes Y(t)=f(X(t)) for some simple Borel functions f(·).