On the feller–dynkin and the martingale property of one-dimensional diffusions
Abstract: We show that a one-dimensional regular continuous Markov process X with scale function s is a Feller–Dynkin process precisely if the space transformed process s(X) is a martingale when stopped at the boundaries of its state space. As a consequence, the Feller–Dynkin and the martingale property are equivalent for regular diffusions on natural scale with open state space. By means of a counterexample, we also show that this equivalence fails for multidimensional diffusions. Moreover, for Itô diffusions we discuss relations to Cauchy problems
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Notes
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Electronic communications in probability. - 28 (2023) , 1-15, ISSN: 1083-589X
- DOI
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10.1214/23-ecp524
- URN
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urn:nbn:de:bsz:25-freidok-2536436
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:52 PM CET
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Associated
- Criens, David
- Universität
Time of origin
- 2024
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