Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Dynamics of non-stationary processes that follow the maximum of the Renyi entropy principle. / Shalymov, Dmitry S.; Fradkov, Alexander L.
в: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Том 472, № 2185, 20150324, 01.01.2016.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Dynamics of non-stationary processes that follow the maximum of the Renyi entropy principle
AU - Shalymov, Dmitry S.
AU - Fradkov, Alexander L.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Renyi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Renyi 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 Renyi distribution is examined.
AB - We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Renyi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Renyi 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 Renyi distribution is examined.
KW - Renyi entropy
KW - maximum entropy principle
KW - Renyi distribution
KW - speed-gradient principle
KW - SPEED-GRADIENT
KW - DIVERGENCE MEASURES
KW - INFORMATION-THEORY
KW - COMPLEX FLUIDS
KW - THERMODYNAMICS
U2 - 10.1098/rspa.2015.0324
DO - 10.1098/rspa.2015.0324
M3 - статья
VL - 472
JO - PROC. R. SOC. - A.
JF - PROC. R. SOC. - A.
SN - 0950-1207
IS - 2185
M1 - 20150324
ER -
ID: 7551853