Martin representation for α-harmonic functions

• Autorzy: Michalik K. , Samotij K.
• Języki publikacji: EN

Abstrakty

EN

Let D be a nonempty open bounded subset of R^d, d ≥2, and let 0 < α < 2. For α-harmonic functions on D vanishing outside D an analogue of the Martin representation for harmonic functions is derived.

Słowa kluczowe

EN

potential theory; Markov processes; Martin boundary

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 1
• Strony: 75--91
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Michalik K.

• Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland

autor

Samotij K.

• Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland

Bibliografia

• [1] R. F. Bass, Probabilistic Techniques in Analysis, Springer, New York 1995.
• [2] R. F. Bass and M. Cranston, Exit times for symmetric stable processes in Rd, Ann. Probab. 11 (1983), pp. 578-588.
• [3] R. M. Blumenthal and R. K. Getоor, Markov Processes and Potential Theory, Academic Press, New York 1969.
• [4] K. Bogdan, The boundary Harnack principle for fractional Laplacian, Studia Math. 123 (1997), pp. 43-80.
• [5] K. Bogdan, Representation of α-harmonic functions in Lipschitz domains, Hiroshima Math. J. 29 (1999), pp. 227-243.
• [6] M. Brelot, On Topologies and Boundaries in Potential Theory, Springer, 1971.
• [7] T. Kulczycki, Exit time and Green function of cone for symmetric stable processes, Probab. Math. Statist. 19 (1999), pp. 337-374.
• [8] H. Kunita and T. Watanabe, Markov processes and Martin boundaries, Part /, Illinois J. Math. 8 (1964), pp. 485-526.
• [9] N. S. Landkof, Foundations of Modern Potential Theory, Springer, Berlin 1969.