Abstract
We present the foundations of the theory of nonhomogeneous Markov processes in general state spaces and we give a survey of the fundamental papers in this topic. We consider the following questions:
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1.
The existence of transition functions for a Markov process.
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2.
The construction of regularization of processes.
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3.
The properties of right and left processes: the strict Markov property, the behavior of excessive functions, etc.
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4.
The relation of right and left processes with dual homogeneous processes and the application of the results of the nonhomogeneous theory to dual homogeneous processes, etc.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Vol. 20, pp. 37–178, 1982.
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Kuznetsov, S.E. Nonhomogeneous Markov processes. J Math Sci 25, 1380–1498 (1984). https://doi.org/10.1007/BF01255812
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DOI: https://doi.org/10.1007/BF01255812