Asymptotic Methods for Stability Analysis of Markov Evolution Families Based on Diffusion Approximation of Slow Motion

Proceedings of the 12th International Conference on Applied Mathematics (APLIMAT 2013) 2013
Jevgeņijs Carkovs, Aija Pola

Asymptotic method for stability analysis of linear differential equations with matrix-function frequently switched by fast random evolution and ergodic Markov process is presented. The proposed method is based on diffusion approximation of linear slow motion and random evolution family applying averaging procedure with respect to time and the invariant measure of the Markov process. It is proved that exponential /^-stability of the resulting linear stochastic equation non-dependent on time and switched Markov process is sufficient for exponential ^-stability of the initial random system.

Atslēgas vārdi
Random Dynamical Syastems; Diffusion Approximation; Stochastic Stabi¬lity: Averaging Procedures

Carkovs, J., Pola, A. Asymptotic Methods for Stability Analysis of Markov Evolution Families Based on Diffusion Approximation of Slow Motion. No: Proceedings of the 12th International Conference on Applied Mathematics (APLIMAT 2013), Slovākija, Bratislava, 5.-7. februāris, 2013. Bratislava: Slovak University of Technology, 2013, P12-1.-P12-6.lpp. ISBN 978-80-227-3865-1.

Publikācijas valoda
English (en)