Geodesic
On Feller semigroups associated with one-dimensional diffusion processes with membranes
Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 31-44

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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: parabolic potential
Mots-clés : Diffusion process, conjugation problem. 
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     author = {B. I. Kopytko and R. V. Shevchuk},
     title = {On {Feller} semigroups associated with one-dimensional diffusion processes with membranes},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {31--44},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a3/}
}
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B. I. Kopytko; R. V. Shevchuk. On Feller semigroups associated with one-dimensional diffusion processes with membranes. Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 31-44. http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a3/