Abstract
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.
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