一类部分可观测非平稳扩散过程的最佳估计与随机分析

THE OPTIMAL ESTIMATION AND RANDOM ANALYSIS ABOUT A KIND OF APART OBSERVING UNSTATIONARY DIFFUSE PROCESS

在概率空间（Ω，Ｐ）中，建立了一类部分可观测非平稳随机扩散Ｍａｒｋｏｖ过程，进而研究了这类随机过程（θｔ，ξｔ）。０≤ｔ≤Ｔ的不可观测分量θｔ依观测结果ξｓ，ｓ≤ｔ的最佳状态估计问题，探讨了在这随机函数中最佳估计解的唯一性，得到了用于估计二维非平稳随机扩散Ｍａｒｋｏｖ过程不可观测分量最佳状态的最佳非线性滤波方程，从而满意地解决了此类随机过程不可观测分量的参数估计问题．

This article sets up a kind of apart observing unstationary Markov's randomdiffusion process in the probability space (Ω, P). And it studies the optimal state estimation problem about this kind of random-process(θs,ξt),0≤t≤T non-measurable component θt according to the measurable resull ξs,s≤t. It also inguires into the uniqueness of the optimal 1estimation solution to this kind of random function and gets the optimal nonlinear filter eguation which is used to estimating the optimal state about non-measutable component of twodimension unstationary Markov's random-diffusion process. Thus it solves the parameter estimation problem of the random process non-measurable component satisfactorily.