Continuous-time, constant causative Markov chains

AbstractThe definition of a constant causative Markov chain is extended to the continuous-time case. Such chains are nonhomogeneous and are found to have intensity matrices of the form Q(t) = tC + Q. Ergodicity is investigated resulting in an extension to continuous-time of a version of Lipstein's conjecture for constant causative chains. In the case where Q and C commute the irreducibility and ergodicity of the constant-causative chain can be directly related to that of two corresponding discrete-time, homogeneous chains, P̃ = I + Q / q and R̃ = I + C /c