Bessel potentials, Green functions and exponential functionals on half-spaces

• Autorzy: Byczkowski T. , Ryznar M. , Byczkowska H.
• Języki publikacji: EN

Abstrakty

EN

The purpose of the paper is to provide precise estimates for the Green function corresponding to the operator (I—Δ)^α/2, 0 <α< 2. The potential theory of this operator is based on Bessel potentials J_α=(I—Δ) ^-α/2. In probabilistic terms it corresponds to a subprobabilistic process obtained from the so-called relativistic a-stable process. We are interested in the theory of the killed process when exiting a fixed half-space. The crucial role in our research is played by (recently found) an explicit form of the Green function of a half-space. We also examine properties of some exponential functionals corresponding to the operator (I—Δ) ^α/2.

Słowa kluczowe

EN

Bessel potentials; Riesz kernels; relativistic process; stable process; Poisson kernel; Green function; half-space

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 1
• Strony: 155--173
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Byczkowski T.

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology,Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Ryznar M.

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology,Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Byczkowska H.

• Institute of Mathematics and Computer Sciences, Wrocław University of Technology,Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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• [5] T. Byczkowski, M. Ryznar and J. Małecki, Bessel potentials, hitting distributions and Green functions, preprint.
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