四重马氏过程的一些统计性质

Some Statistical Properties of the 4-ple Markov Processes

设｛０ｘ（ｔ），ｔ∈Ｒ￣（＋）｝由维纳随矾积分所定义的四重马氏正态过程，这里｛Ｂ（ｔ），ｔ∈￣（＋）｝是标准布朗运动过程。若随机过程｛ｘ（ｔ）｝被一有界ｆｆｅｒｅｌ可测函数ｆ所变换，则将得到随机泛函ｆ（ｘ（ｔ）），即得到新的随机过程，把它记为Ｙ（ｔ），也就是说Ｙ（ｔ）＝ｆ（Ｘ（ｔ））．作者在本文中首先粗略地研讨四重马氏过程的一些统计特性以及与此有关的问题。其次，对较简单一类Ｂｏｒｅｌ可测函数ｆ，探讨随机泛函ｆ（ｘ（ｔ））的最佳非线性预测量。

Let {x(t),t∈R￣(+)}be a 4-ple Markov Gaussian process which is defined by theWiener integralwhere{B(t),t∈R￣(+)}is a standard Brownian motion process.If the stochastic process{(t)}is transformed bV a bounded Borel measurable function f,then we obtain a stochasticfunctional f(x(t)),that is we shall get a new stochastic process which denoteS by Y(t),namely Y(t)=f(x(t))In this paper,the author at first roughly discussed some statistlcalproperties of the 4-ple Markov process{x(t)}and so forth.In addition, the author dealswith the best nonlinear predictors of the stochastic functionalsf(x(t))for some simpleBorel measurable functions f.