完备概率空间中一类非平稳过程泛函结构的随机分析

STOCHASTIC ANALYSIS O FUNSTIONAL STRUCTURE OF NONSTATIONARY RANDOM PROCESS IN COMPLETE PROBABILITY SPACE

本文运用鞅理论与随机分析方法讨论了完备概率空间中一类非平稳过程的泛函结构,得到了Wiener过程、扩散过程与Ito过程及其在Gauss情形下泛函结构的一系列重要结果,这对于解决该类可观测随机过程的最佳非线性滤波具有很大意义。

This article discusses the functional structure of a nonstationary random process on the complete probability space with martingale theory and stochastic analysis process, and ob-tains Wiener processes, diffusion processes, Ito processes and a series of important results ofthe functional structure under Gauss Conditions. It is important for solving the optimum non-linear filters of such measurable stochastic process.