Structural properties of Markov chains with weak and strong interactions (Q1275960)

A class of Markov chains with finite number of states and continuous time parameter is examined. Their generators are in the form \(\varepsilon ^{-1}A(t)+B(t)\) where the block-diagonal matrix function \(A(t)\) corresponds to the fast motion and \(B(t)\) governs the slow components. When \(\varepsilon \) tends to zero, the asymptotic behaviour is described in the \(L_2\) and weak topologies. The idea is to approximate by an aggregate process and to work out error bounds.