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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Semigroups of operators that describe a Feller process on the line, which is the result of pasting together two diffusion processes


Authors: P. P. Kononchuk and B. I. Kopytko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 87-97
MSC (2010): Primary 60J60
Published electronically: July 31, 2012
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Abstract: We use the method of the classical potential theory to construct the semigroup of operators that describe a Feller process on the line by pasting together two diffusion processes that satisfy a nonlocal Feller-Wentzell type condition for the pasting.


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Additional Information

P. P. Kononchuk
Affiliation: Department of Higher Mathematics, Faculty for Mechanics and Mathematics, L’viv National Ivan Franko University, Universytets’ka Street 1, L’viv 79000, Ukraine
Email: p.kononchuk@gmail.com

B. I. Kopytko
Affiliation: Department of Higher Mathematics, Faculty for Mechanics and Mathematics, L’viv National Ivan Franko University, Universytets’ka Street 1, L’viv 79000, Ukraine
Email: bohdan.kopytko@gmail.com

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00868-5
PII: S 0094-9000(2012)00868-5
Keywords: Diffusion processes, discontinuities of trajectories, analytic methods, method of potential
Received by editor(s): September 27, 2010
Published electronically: July 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society