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多谢多谢 不过班竹说的好像是stationary stochastic process 阿？ 两者一样吗？
估计是我没说清楚 我本意是progressive measurable process 找到了wiki上的一个词条 能否再帮忙看一下
 | This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. (January 2009) |
In mathematics, progressive measurability is a property of stochastic processes. A progressively measurable process cannot "see into the future", but being progressively measurable is a strictly stronger property than the notion of being an adapted process.
Let
be a probability space; 
be a measurable space, the state space; 
be a filtration of the sigma algebra 
; 
be a stochastic process (the index set could be [0,T] or 
instead of 
). The process X is said to be progressively measurable (or simply progressive) if, for every time t, the map ![[0, t] \times \Omega \to \mathbb{X}](http://upload.wikimedia.org/math/3/2/3/323e2c2893f050592446f7fa86c8122c.png)
defined by 
is ![\mathrm{Borel}([0, t]) \otimes \mathcal{F}_{t}](http://upload.wikimedia.org/math/d/e/e/deee56d4ba6263261cca75865935a931.png)
-measurable. This implies that X is 
-adapted.
Also, we say that a subset 
is progressively measurable if the process Xs(ω): = χP(s,ω) is progressively measurable in the sense defined above. The set of all such subsets P form a sigma algebra on 
, denoted Prog, and a process X is progressively measurable in the sense of the previous paragraph if, and only if, it is Prog-measurable.
![X : [0, T] \times \Omega \to \mathbb{R}^{n}](http://upload.wikimedia.org/math/5/e/a/5eac274cdacec2c5263c68d0c4bd797b.png)
for which the [[Ito integral 
![L^2 ([0, T] \times \Omega; \mathbb{R}^n)\,](http://upload.wikimedia.org/math/0/8/0/0803a5ffe512b48b4ac983f2cf413fe7.png)
. 
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