<abstract xmlns="http://www.w3.org/1999/xhtml">This paper deals with linear impulse dynamical systems on ℝd whose parameters depend on an ergodic piece-wise constant Markov process with values from some phase space <italic>𝕐</italic> and on a small parameter ɛ. Trajectories of Markov process x(t,y)∈ ℝd satisfy a system of linear differential equations with close to constant coefficients on its continuity intervals, while its phase coordinate changes discontinuously when Markov process switching occur. Jump sizes depend linearly on the phase coordinate and are proportional to the small parameter ɛ. We propose a method and an algorithm for choosing the base 𝔹(t,y) of the space ℝd that provides approximation of average phase trajectories <bold>E</bold>{x(t,y)} by a solution of a system of linear differential equations with constant coefficients.</abstract>

This paper deals with linear impulse dynamical systems on ℝd whose parameters depend on an ergodic piece-wise constant Markov process with values from some phase space 𝕐 and on a small parameter ɛ. Trajectories of Markov process x(t,y)∈ ℝd satisfy a system of linear differential equations with close to constant coefficients on its continuity intervals, while its phase coordinate changes discontinuously when Markov process switching occur. Jump sizes depend linearly on the phase coordinate and are proportional to the small parameter ɛ. We propose a method and an algorithm for choosing the base 𝔹(t,y) of the space ℝd that provides approximation of average phase trajectories E{x(t,y)} by a solution of a system of linear differential equations with constant coefficients.

Reducibility by Moments of Linear Impulse Markov Dynamical Systems with Almost Constant Coefficients

Department of Theory of Probability and Mathematical Statistics, Rīga Technical University, Kaļíu iela 1, Rīga, LV-1658, LATVIA

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper deals with linear impulse dynamical systems on ℝd whose parameters depend on an ergodic piece-wise constant Markov process with values from some...

Reducibility by Moments of Linear Impulse Markov Dynamical Systems with Almost Constant Coefficients

Published Online: Apr 04, 2016

Page range: 34 - 40

Received: Sep 27, 2015

DOI: https://doi.org/10.1515/prolas-2016-0006

Keywords
dynamical system, Markov process, reducibility, perturbation theory

© 2016 Jevgeņijs Carkovs et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Reducibility by Moments of Linear Impulse Markov Dynamical Systems with Almost Constant Coefficients

Published Online: Apr 04, 2016

Page range: 34 - 40

Received: Sep 27, 2015

DOI: https://doi.org/10.1515/prolas-2016-0006

Keywordsdynamical system, Markov process, reducibility, perturbation theory

© 2016 Jevgeņijs Carkovs et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
dynamical system, Markov process, reducibility, perturbation theory