On pasting together two inhomogeneous diffusion processes on a line with the general Feller–Wentzell conjugation condition

B. I. Kopytko, R. V. Shevchuk
Theory of Stochastic Processes
Vol.17 (33), no.2, 2011, pp.55-70
By the method of classical potential theory, we obtain an integral representation for the two-parameter semigroup of operators that describes the inhomogeneous Feller process on a line being a result of pasting together two diffusion processes with the general Feller–Wentzell conjugation condition.