scholarly journals Analytical Solution of Kolmogorov Equations for Four-Condition Homogenous, Symmetric and Ergodic System

2014 ◽  
Vol 04 (10) ◽  
pp. 497-500 ◽  
Author(s):  
Victor V. Kravets ◽  
Konstantin M. Bass ◽  
Vladimir V. Kravets ◽  
Larisa A. Tokar
Keyword(s):  
Analytical Solution ◽  
Ergodic System ◽  
Kolmogorov Equations

scholarly journals Model of time-varying linear systems and Kolmogorov equations

2015 ◽  
Vol 25 (2) ◽  
pp. 201-214
Author(s):  
Assen V. Krumov
Keyword(s):  
Analytical Solution ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Original System ◽  
Approximate Model ◽  
Time Varying ◽  
Kolmogorov Equations ◽  
Varying Coefficients ◽  
Method Of Solution ◽  
Time Varying Coefficients

Abstract In the paper an approximate model of time-varying linear systems using a sequence of time-invariant systems is suggested. The conditions for validity of the approximation are proven with a theorem. Examples comparing the numerical solution of the original system and the analytical solution of the model are given. For the system under the consideration a new criterion giving sufficient conditions for robust Lagrange stability is suggested. The criterion is proven with a theorem. Examples are given showing stable and non stable solutions of a time-varying system and the results are compared with the numerical Runge-Kutta solution of the system. In the paper an important application of the described method of solution of linear systems with time-varying coefficients, namely analytical solution of the Kolmogorov equations is shown.

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