Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient
Abstract
We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.
Keywords
Cite
@article{arxiv.1006.4128,
title = {Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient},
author = {A. N. Gorban},
journal= {arXiv preprint arXiv:1006.4128},
year = {2011}
}
Comments
The final journal version