From empirical data to time-inhomogeneous continuous Markov processes.
From empirical data to time-inhomogeneous continuous Markov processes.
复制标题
从经验数据到时间不均匀的连续马尔可夫过程。
作者：
P. Lencastre;F. Raischel;T. Rogers;P. Lind
给出了一种检验离散随机转移矩阵的连续生成是否存在的方法。通常，现有的确定连续马尔可夫过程存在性的方法是基于只存在时间齐次发生器的假设。本文基于包含充分必要条件的新的数学命题，对时间非均匀性进行了系统的扩展，并将其应用于数值数据。讨论了发生器存在性的严格数学结果与其计算实现之间的桥梁问题。我们的检测算法显示在超过60%的测试矩阵中是有效的，通常是80%到90%，对于那些（非齐次）生成器矩阵的估计如下。对于三维循环矩阵的特殊情况，我们也解析地解决了嵌入问题。最后，简要讨论了我们的框架对不同领域问题的可能应用。
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.