On Reducibility of Linear Markov Switched Difference Equations

AIP Conference Proceedings: International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014) 2015
Jevgeņijs Carkovs, Jolanta Goldšteine

The paper deals with the system of linear difference equations in Rd with the right part switched by homogeneous ergodic Markov chain on the compact phase space Y. We prove that the shift operator family for the conditional first moments of the solutions possess a semigroup property and derive the infinitesimal generator for this semigroup. This approach permits to propose convenient to application algorithm for asymptotic analysis of the equations with near to constant coefficients. We have proved that for sufficiently small Markov type perturbations there exists such a matrix Λ that the first moments of the solutions have an asymptotic close to Λtx.

Keywords
Stochastic difference equations, Markov switching, linear difference equation reducibility
DOI
10.1063/1.4913060
Hyperlink
http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4913060

Carkovs, J., Goldšteine, J. On Reducibility of Linear Markov Switched Difference Equations. In: AIP Conference Proceedings: International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), Greece, Rhodes, 22-28 September, 2014. Melville: AIP Publishing, 2015, pp.850005-1-850005-4. ISBN 978-0-7354-1287-3. ISSN 0094-243X. e-ISSN 1551-7616. Available from: doi:10.1063/1.4913060

Publication language
English (en)