On cubic stochastic operators and processes *

Algebra, Analysis and Quantum Probability

Mamurov, B.J.^1 ; Rozikov, U.A.^2

Bukhara State Medical Institute, Navoi str., 1, Bukhara, Uzbekistan^1

Institute of Mathematics, National University of Uzbekistan, Do'rmon Yo'li str., 29, Tashkent

100125, Uzbekistan^2

关键词: Continuous-time;    Finite dimensional;    Measurable space;    Probability measures;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012017/pdf
DOI  :  10.1088/1742-6596/697/1/012017

来源: IOP

【 摘 要 】

In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The measurable space can be given on a finite or continual set. The finite case has been investigated before. So here we mainly work on the continual set. We give a construction of a CSO and show that dynamical systems generated by such a CSO can be studied by studying of the behavior of trajectories of a CSO given on a finite dimensional simplex. We define a CSP and drive differential equations for such CSPs with continuous time.