论文标题
由相关误差驱动的随机过程的图形建模
Graphical modeling of stochastic processes driven by correlated errors
论文作者
论文摘要
我们研究一类代表随机过程中局部独立性结构的图形，允许相关的误差过程。几个图形可以编码相同的本地独立性，我们表征了图形的等效类。在最坏的情况下，我们特征中的条件数量会随着图表中的节点设置的大小而增长的级别分析。我们表明，决定马尔可夫等效性是综合性的，这表明我们的特征在基本上无法改善。在多元Ornstein-uhlenbeck过程中，我们证明了全球马尔可夫财产，该过程由相关的布朗尼动作驱动。
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.
