B. I. Kopytko, R. V. Shevchuk, “On Feller semigroups associated with one-dimensional diffusion processes with membranes”, Theory Stoch. Process., 2016, Volume 21(37), Issue 1,Pages <nobr>31

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On Feller semigroups associated with one-dimensional diffusion processes with membranes

B. I. Kopytko^a, R. V. Shevchuk^b

^a Ivan Franko National University of Lviv, Lviv, Ukraine; Institute of Mathematics, Czestochowa University of Technology, Czestochowa, Poland
^b Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

Abstract: By analytical method we obtain the integral representation of a two-parameter semigroup of operators associated with Feller process on a line which is a result of pasting together given diffusions at finite number of fixed points. The behavior of this process at each point of pasting together is described by Feller-Wentzell conjugation condition containing the integral term (nonlocal component).

Keywords: Diffusion process, parabolic potential, conjugation problem.

MSC: Primary 60J60

Language: English