一类Gauss随机扩散过程方程组解的连续惟一及相合性分析

The Continuity and Unigueness of the Solution for the Simultaneous Equations of a Class of Gaussian Diffusion Process and Analysis of Consistency

在完备概率空间(Ω,F,P)中,讨论了一类带非超前泛函的条件Gauss随机扩散过程方程组解的连续惟一性及其具有连续惟一强解的条件,并在方程组存在相应连续惟一强解的情况下,讨论了σ-代数Ftξ和Ftξ0,-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ξ相同“信息”的结果Ftξ=Ft0ξ,-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.

In complete measure space （Ω,F, p）, the continuity and uniqueness of the solution for the simultaneous equations of a class Graussian diffusion process with non-advanced function and the requirements which make such a solution possible were discussed. After a thorough discussion of the congruent matrices of σ-algebraric F^ti and F^tio,^W on the condition that the system of equations has a corresponding sole strong solution,the conclusion F^ξi=F^ξiσ,^W,0≤t≤T was drew, that the renewal process W^-= （ W^-t ）, t≥0,contains the same information as the measurable process ξ does. This conclusion is significant for further research on some optimal control problems in such process.