Mean Square Lyapunov Exponents for Linear Markov Switched Difference Equations with near to Constant Coefficients

Proceedings of the 14th Conference on Applied Mathematics APLIMAT 2015 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 {yt } on the compact phase space Y. We prove that there exists such the linear continuous operator A on the space of symmetric d xd-matrix-function q(y) that for any t =1,2,..., y, and x one can write the equality E{(q(yt)xt; xt) /y0 = y; x0 = x} = E{(Atq)(y)x; x)}. This approach permits to derive such the basis matrix B(y) in the space Rd that the random process zt = B(yt)xt has the same mean square Lyapunov exponents as the solution of the above equation x(t) and to propose convenient to application algorithm for asymptotic analysis of the equations with near to constant coefficients.

Keywords
Markov difference equations, Markov switching, linear difference equation

Carkovs, J., Goldšteine, J. Mean Square Lyapunov Exponents for Linear Markov Switched Difference Equations with near to Constant Coefficients. In: Proceedings of the 14th Conference on Applied Mathematics APLIMAT 2015, Slovakia, Bratislava, 3-5 February, 2015. Bratislava: Slovak University of Technology in Bratislava, Publishing House of STU, 2015, pp.158-166. ISBN 978-80-227-4143-3.

Publication language
English (en)