Evolution of non-stationary processes and some maximum entropy principles

AbstractThis paper studies, by using the speed-gradient principle, the evolution of non-stationary processes in the context of maximization of Varma, weighted Rényi, weighted Varma and Rényi-Tsallis of order α entropies.

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Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0324 ◽

2016 ◽

Vol 472 (2185) ◽

pp. 20150324 ◽

Cited By ~ 7

Author(s):

Dmitry S. Shalymov ◽

Alexander L. Fradkov

Keyword(s):

Limit Distribution ◽

Mass Conservation ◽

Random Variable ◽

Renyi Entropy ◽

Rényi Entropy ◽

Stationary Processes ◽

Entropy Principle ◽

Gradient Principle ◽

Probability Density Function Pdf ◽

Speed Gradient

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.

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Speed-gradient principle for description of transient dynamics in systems obeying maximum entropy principle

10.1063/1.3573643 ◽

2011 ◽

Cited By ~ 1

Author(s):

Alexander Fradkov ◽

Anton Krivtsov ◽

Ali Mohammad-Djafari ◽

Jean-François Bercher ◽

Pierre Bessiére

Keyword(s):

Maximum Entropy ◽

Maximum Entropy Principle ◽

Transient Dynamics ◽

Entropy Principle ◽

Gradient Principle ◽

Speed Gradient

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GENERIC and Speed-Gradient Principle

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2018.12.104 ◽

2018 ◽

Vol 51 (33) ◽

pp. 121-126

Author(s):

Dmitry S. Shalymov ◽

Alexander L. Fradkov

Keyword(s):

Gradient Principle ◽

Speed Gradient

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Dynamics of differential entropy maximization process via the Speed Gradient principle

2015 23rd Mediterranean Conference on Control and Automation (MED) ◽

10.1109/med.2015.7158787 ◽

2015 ◽

Author(s):

Dmitry S. Shalymov ◽

Alexander L. Fradkov

Keyword(s):

Differential Entropy ◽

Entropy Maximization ◽

Gradient Principle ◽

Speed Gradient

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Simulation of MEPP via speed-gradient principle

2015 57th International Symposium ELMAR (ELMAR) ◽

10.1109/elmar.2015.7334509 ◽

2015 ◽

Author(s):

Dmitry S. Shalymov ◽

Alexander L. Fradkov

Keyword(s):

Gradient Principle ◽

Speed Gradient

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Maximum Non-Extensive Entropy Block Bootstrap for Non-stationary Processes

L Actualité économique ◽

10.7202/1036916ar ◽

2016 ◽

Vol 91 (1-2) ◽

pp. 115-139 ◽

Cited By ~ 1

Author(s):

Michele Bergamelli ◽

Jan Novotný ◽

Giovanni Urga

Keyword(s):

Time Series ◽

Monte Carlo ◽

Maximum Entropy ◽

Rank Correlation ◽

Monte Carlo Analysis ◽

Stationary Processes ◽

Block Bootstrap ◽

Finite Sample ◽

Tail Behaviour ◽

Finite Sample Properties

In this paper, we propose a novel entropy-based resampling scheme valid for non-stationary data. In particular, we identify the reason for the failure of the original entropy-based algorithm of Vinod and López-de Lacalle (2009) to be the perfect rank correlation between the actual and bootstrapped time series. We propose the Maximum Entropy Block Bootstrap which preserves the rank correlation locally. Further, we also introduce the Maximum non-extensive Entropy Block Bootstrap to allow for fat tail behaviour in time series. Finally, we show the optimal finite sample properties of the proposed methods via a Monte Carlo analysis where we bootstrap the distribution of the Dickey-Fuller test.

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Dynamics of the f-divergence minimization processes based on the speed-gradient principle

2016 IEEE Conference on Norbert Wiener in the 21st Century (21CW) ◽

10.1109/norbert.2016.7547431 ◽

2016 ◽

Cited By ~ 1

Author(s):

Dmitry S. Shalymov ◽

Alexander L. Fradkov

Keyword(s):

Gradient Principle ◽

Divergence Minimization ◽

Speed Gradient

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Stochasting modeling of planetary ring systems

International Astronomical Union Colloquium ◽

10.1017/s025292110010154x ◽

1984 ◽

Vol 75 ◽

pp. 461-469 ◽

Cited By ~ 1

Author(s):

Robert W. Hart

Keyword(s):

Maximum Entropy ◽

Ring System ◽

The Sun ◽

Ultimate State ◽

Interparticle Interactions ◽

Ring Systems ◽

First Order ◽

Planetary Ring ◽

Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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