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Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point

Kopytko B., Shevchuk R.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 1

55--68

By the method of classical potential theory, we obtain the integral representation of the two-parameter operator semigroup that describes the inhomogeneous Feller process on a closed interval [ r1,r2 ] that is a result of pasting together two diffusion processes given on ( r1,r, ) and ( r, r2 ), respectively, where - ∞ < r1 < r < r2 <∞ .