论文标题
自相似的高斯马尔可夫流程
Self-similar Gaussian Markov processes
论文作者
论文摘要
我们表征了所有多维真实的自相似高斯马尔可夫过程。出现了三种类型的协方差矩阵函数：白色噪声类型函数，可以通过连续矩阵半群来表达的协方差，以及基于Cauchy功能方程的非连续解的协方差。表征后者的需要我们对非连续矩阵半群的表示理论产生一些结果，这些矩阵半群是在伴侣论文中提出的。在尺寸1中，除了白噪声外，自相似的高斯马尔可夫过程还减少了两参数的时间变化的布朗尼动作。该观察结果简化了文献中发现的混凝土过程的非马克维亚性的几种证明。
We characterize all multi-dimensional real self-similar Gaussian Markov processes. Three types of covariance matrix functions occur: white-noise type functions, covariances that can be expressed by continuous matrix semigroups, and covariances based on non-continuous solutions of Cauchy's functional equation. Characterizing the latter requires us to develop some results on the representation theory of non-continuous matrix semigroups, which are presented in a companion paper. In dimension one, besides white noise, the self-similar Gaussian Markov processes reduce to a two-parameter family of time-changed Brownian motions. This observation simplifies several proofs of non-Markovianity of concrete processes found in the literature.
