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One-dimensional diffusion processes in half-bounded domains with reflection and a possible jump-like exit from a moving boundary

Kopytko B., Shevchuk R.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

71-82

By the method of the classical potential theory, we construct the two-parameter Feller semigroup of operators associated with such a diffusion phenomenon on a half-line with a moving boundary where either a reflection or jump phenomenon occurs at a boundary point.

One-dimensional diffusions in bounded domains with a possible jump-like exit from a sticky boundary

Kopytko B., Shevchuk R.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 3

101--114

Using analytical methods we obtain the integral representation of a two-parameter Feller semigroup on a closed interval [r1, r2] corresponding to such a diffusion phenomenon that sticking, partial reflection, absorption and jump phenomena occur at the endpoints r1, r2 and at some interior point r ∈ (r1,r2).

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 <∞ .