Abstract
In this article, we mainly discuss some potential theory in the framework of right Markov processes. We introduce the concept of α–excessive function, α–recurrence and α–transience for right processes with α ≤ 0, and give a thorough investigation.
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Sharpe, M.: General Theory of Markov Processes, Academic Press, San Diego, 1988
Getoor, R. K.: Transience and Recurrence of Markov Processes, in “Séminaire de probabilité XIV (univ. Strasbourg).” Lecture notes in Math., Springer, Berlin, Heidelberg, New York, 784, 397–409 (1980)
Blumenthal, R. M., Getoor, R. K.: Markov Processes and Potential Theory, Academic Press, New York, 1968
Zhao, M. Z., Zhang, H. Z.: The weighted transience and recurrence of Markov processes. Acta Mathematica Sinica, English Series, 22(6), (2006)
Zhao, M. Z., Ying, J. G.: Polynomial recurrence for Lévy processes. Chin. Ann. Math., 25B(2), 165–174 (2004)
Zhang, H. Z., Zhao, M. Z., Ying, J. G.: α-transience and α-recurrence for random walks and Lévy processes. Chin. Ann. Math., 26B(1), 127–142 (2005)
Getoor, R. K.: Excessive Measures, Birkhäuser, Boston–Basel–Berlin, 1990
Anderson, W. J.: Continous-Time Markov Chains: An Applications-Oriented Approach, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, 1991
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Research supported in part by NSFC 10271109
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Zhao, M.Z., Ying, J.G. α–Transience and α–Recurrence of Right Processes. Acta Math Sinica 22, 1413–1424 (2006). https://doi.org/10.1007/s10114-005-0667-5
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DOI: https://doi.org/10.1007/s10114-005-0667-5