一类带条件随机信号的随机扩散过程连续唯一强解的随机分析

运用随机优化分析与随机递推滤波方法讨论了一类带条件随机信号的随机扩散过程Ftζ-可测解的连续唯一性及其具有连续唯一强解的条件,并在该扩散过程存在相应连续唯一强解的情况下,讨论了σ-代数Ftζ和Ftζ0,w-的相合性,得到了关于更新过程-W=(-Wt),t≥0包含有与可观测过程ζ相同"信息"的深入结果Ftζ=Ftζ0,w-,0≤t≤T,该结论对于进一步研究此类过程的某些最优控制问题具有重要意义.

Random analysis of the continuous sole strong solution of the random diffusion process of a class of the random signals with conditions

The continuous uniqueness of Ftζ- measurable solution of the random diffusion process of a class of random signals with conditions and the conditions under which the random diffusion process has the continuous sole strong solution are studied by means of random optimization analysis and random recursive filtering.The consistency of σ-algebraic Ftζ and Ftζ0, is discussed under the condition of the diffusion process having the continuous sole strong solution,and the conclusion is draw that the renewal process =(t),t≥0 contains the same information as the measurable process ζ does,that is,Ftζ=Ftζ0,.This conclusion is significant to the further research in some optimal control problems of such process.