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arXiv · 2004.01702

Quadratic stochastic processes of type $(\sigma|\mu)$

B. J. Mamurov·U. A. Rozikov·S. S. Xudayarov
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Abstract

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 $\sigma$) stochastic cubic matrices satisfying an analogue of Kolmogorov-Chapman equation (KCE) with respect to a fixed multiplications (called $\mu$) 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 $(\sigma | \mu)$. 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).

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B. J. Mamurov, U. A. Rozikov, S. S. Xudayarov. 2020-04-03. Quadratic stochastic processes of type $(\sigma|\mu)$. https://arxiv.org/abs/2004.01702

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