On L ₁-weak ergodicity of nonhomogeneous discrete Markov processes and its applications

In the present paper we investigate the L ₁-weak ergodicity of nonhomogeneous discrete Markov processes with general state spaces. Note that the L ₁-weak ergodicity is weaker than well-known weak ergodicity. We provide a necessary and sufficient condition for such processes to satisfy the L ₁-weak ergodicity. Moreover, we apply the obtained results to establish L ₁-weak ergodicity of discrete time quadratic stochastic processes. As an application of the main result, certain concrete examples are also provided.