相关误差驱动随机过程的图形建模
Graphical modeling of stochastic processes driven by correlated errors
摘要：
我们研究了一类图，表示局部独立结构的随机过程，允许相关的错误过程。几个图可以编码相同的局部独立性，我们刻画了这样的等价类的图。在最坏的情况下，在我们的特征的条件的数量增长超多项式作为一个函数的节点集在图中的大小。我们发现，决定马尔可夫等价是coNP-完全的，这表明我们的特征不能得到改善后，大大。本文证明了由相关布朗运动驱动的多变量Ornstein-Uhlenbeck过程的全局马尔可夫性。
英文摘要：
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolynomially as a function of the size of the node set in the graph. We show that deciding Markov equivalence is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.
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