四重马氏平稳过程的非线性预测问题(英文)

Non-linear Prediction Problemof Quadruple Markov Stationary Processes

假设{X(t),t∈R1}是由广义Wiener随机积分所定义的四重马氏平稳过程.首先粗略地研讨了四重马氏平稳过程{X(t),t∈R1}及其均方导数的一些概率性质.其次,如果这随机过程{X(t),t∈R1}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)).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,给出了非线性均方预测的理论依据和实例.

In this paper, the authors at first roughly discuss some probabilistic properties of the quadruple Markov stationary process { X（ t ）, t ∈R^1} t and so forth. Moreover, let { X（ t ）, t ∈R^1} t be a quadruple Markov stationary process which is defined by a generalized Wiener integral. If the stochastic process {X（ t ）, t∈R^1} t is transformed by a bounded Borel measurable function f（· ）, then we obtain a new stochastic process which denotes by Y（ t ）, namely Y（ t ） = f（X（ t ） ）. The authors deal with the nonlinear mean-square predictors of the stochastic processes Y （ t ） = f（ X （ t ） ） for some simple Borel function.s f（·）. The result and example of the non-linear mean-square predictors is given.