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

MathSciNet review:
2857419

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0094-9000-2012-00868-5

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