Modern research often contains stochastic differential equations as the basis of the complex systems model. Modeling of complex systems is often limited to implementations of well-known models with a limited set of the output probability shapes of the of the observed random variable. Application of the well-known stochastic differential equation for the Beta family makes it possible to make models of complex systems flexible to the shape of the output distribution. The article contains stationary stochastic differential equations for the Beta family, obtained on the basis of an asymptotic approximation. The article discusses the features of stationary forms of distribution models included in the stochastic differential equation of the Beta family, and gives expressions for the components of the nonlinear drift velocity and diffusion rate for stationary models of output distributions. In particular, it shows that the properties of subfamilies and the restrictions imposed on the values of the supported random variables depend on the form of setting the family coefficient.
Stochastic differential equations of complex systems and their probability output distributions
PROCEEDINGS OF THE V INTERNATIONAL SCIENTIFIC CONFERENCE ON ADVANCED TECHNOLOGIES IN AEROSPACE, MECHANICAL AND AUTOMATION ENGINEERING: (MIST: Aerospace-V 2023) ; 2023 ; Krasnoyarsk, Russian Federation
AIP Conference Proceedings ; 3102 , 1
27.03.2024
13 pages
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
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