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2 Journal of Applied Mathematics and Computational Mechanics

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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).