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

**B. I. Kopytko, R. V. Shevchuk**

*Theory of Stochastic Processes*

*Vol.21 (37), no.1, 2016, pp.31-44*

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).