摘要
用{x(t),t∈R_1}来表示由随机积分integral from n=-∞ to t (t-r)exp{r-t}dW(r)所确定的二重马氏平稳过程,这里{W(t),t∈R_1)是规范化的广义Wiener过程,设f为有界Borel可测函数,若令Y(t)=f(X(t)),则得二重马氏平稳过程{X(t)}的泛函Y(t)。在本文中,作者首先粗略地研讨了关于二重马氏平稳过程{X(t)}的一些统计特性,然后,较深入地研讨了关于随机泛函Y(t)的一些概率性质,最后又研讨了关于随机泛函Y(t)的均方预测问题,并对几类泛函给出了均方预测量及其均方误差的分析表达式。
Let{X(t), t∈R_1} be the double Markov stationary process, which is given by the following stochastic integral X(t)= integral from n=-∞ to t (t-r)exp{r-t}dW(r), where{W(t), t∈R_1} is a normalized generalized Wiener process,noting that the stochastic process{X(t)} is also Gaussian process. And let f denote a bounded Borel measurable function defined on a measurable space (R_1, F). If the stochastic processes {X(t)} are transformed by function f,that is Y(t)=f(x(t)), we obtain the stochastic functionals Y(t) of the double Markov stationary processes {X(t)}. In this paper, the author deals with sorne probabilistic properties of the double Markov stationary processes {X(t)} and the stochastic functionals f (X(t)). And then the author discusses the non-linear meansquare predictors for the stochastic functionals f(X(t)) and presents some analytical formulas of the non-linear mean-square predictors and the corresponding mean-square errors.
出处
《沈阳化工学院学报》
1992年第4期307-317,共11页
Journal of Shenyang Institute of Chemical Technolgy
关键词
维纳过程
马氏平稳过程
泛函
Wiener process
double Markov stationary process
functionals of double Markov stationary processes
semi-group
mean-square predictor
