title: Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.
abstract: We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.
authors.affiliation: Mathematics and Mechanics Faculty, St Petersburg State University , St Petersburg, Russia.
authors.forename: Dmitry S
authors.identifier: 0000-0002-8794-7306
authors.initials: DS
authors.lastname: Shalymov
authors.affiliation: Mathematics and Mechanics Faculty, St Petersburg State University, St Petersburg, Russia; The Laboratory 'Control of Complex Systems', Institute of Problems of Mechanical Engineering RAS, St Petersburg, Russia.
authors.forename: Alexander L
authors.identifier: 0000-0002-5633-0944
authors.initials: AL
authors.lastname: Fradkov
keywords: Rényi distribution; Rényi entropy; maximum entropy principle; speed-gradient principle