Strong Ergodicity in Nonhomogeneous Markov Systems with Chronological Order

Abstract

In the present, we study the problem of strong ergodicity in nonhomogeneous Markov systems. In the first basic theorem, we relax the fundamental assumption present in all studies of asymptotic behavior. That is, the assumption that the inherent inhomogeneous Markov chain converges to a homogeneous Markov chain with a regular transition probability matrix. In addition, we study the practically important problem of the rate of convergence to strong ergodicity for a nonhomogeneous Markov system (NHMS). In a second basic theorem, we provide conditions under which the rate of convergence to strong ergodicity is geometric. With these conditions, we in fact relax the basic assumption present in all previous studies, that is, that the inherent inhomogeneous Markov chain converges to a homogeneous Markov chain with a regular transition probability matrix geometrically fast. Finally, we provide an illustrative application from the area of manpower planning.

Keywords

• strong ergodicity
• nonhomogeneous Markov systems
• rate of convergence