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).