论文标题
类型$（σ|μ）$的二次随机过程
Quadratic stochastic processes of type $(σ|μ)$
论文作者
论文摘要
我们在连续和离散的时间内构建二次随机过程（QSP）（也称为立方矩阵的马尔可夫过程）。这些是由（固定类型，称为$σ$）给出的动态系统随机立方矩阵，可满足Kolmogorov-Chapman方程（KCE）的类似物，相对于立方矩阵之间的固定乘法（称为$μ$）。 KCE的随机解决方案的存在（每次）的存在提供了称为QSP QSP的QSP的存在，称为$（σ|μ）$。在本文中，我们的目的是构建和研究QSP的轨迹，以专门选择随机立方矩阵的概念和此类矩阵的广泛乘法（称为Maksimov的乘法）。
We construct quadratic stochastic processes (QSP) (also known as Markov processes of cubic matrices) in continuous and discrete times. These are dynamical systems given by (a fixed type, called $σ$) stochastic cubic matrices satisfying an analogue of Kolmogorov-Chapman equation (KCE) with respect to a fixed multiplications (called $μ$) between cubic matrices. The existence of a stochastic (at each time) solution to the KCE provides the existence of a QSP called a QSP of type $(σ| μ)$. In this paper, our aim is to construct and study trajectories of QSPs for specially chosen notions of stochastic cubic matrices and a wide class of multiplications of such matrices (known as Maksimov's multiplications).
