Abstract
A new classification of boundaries is introduced to describe the termination time of a one-dimensional strongly Markovian process near a boundary. Analytic and probabilistic properties of boundaries are presented and compared with the well-known classification.
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E. B. Dynkin, Markov Processes, Springer-Verlag, Berlin (1955).
K. Ito and H. P. McKean, Diffusion Processes and Their Sample Paths, Springer-Verlag, Berlin (1965).
S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York (1981).
P. Mandl, Analytical Treatment of One-Dimensional Markov Processes, Springer-Verlag, Berlin (1968).
J.-U. Löbus, “Generalized second-order differential operators and nonconservative onedimensional quasidiffusions with natural boundaries,” Lect. Notes Contr. and Inform. Si.,96, 164–175 (1987).
J.-U. Löbus, Verallgemeinerte Differentialoperatoren zweiter Ordnung und nichtkonservative eindimensionale Quasidiffusionprozesse, Diss., Jena (1987).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 626–631, May, 1991.
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Löbus, J.U. Classification of boundaries for a diffusion on an open interval. Ukr Math J 43, 580–586 (1991). https://doi.org/10.1007/BF01058544
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DOI: https://doi.org/10.1007/BF01058544