On harmonic measure for Lévy processes

• Autorzy: Sztonyk P.
• Języki publikacji: EN

Abstrakty

EN

Let {X_t} be a Lévy process in R^d, d ≥ 2, with infinite Lévy measure. If {X_t} has no Gaussian component, then the process does not hit the boundary of Lipschitz domain S ⊂ R^d at the first exit time of S under mild conditions on {X_t}. The conditions are met, e.g., if {X_t} is rotation invariant.

Słowa kluczowe

EN

Lévy processes; harmonic measure; Lipschitz domain; Lévy measure

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 2
• Strony: 383--390
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Sztonyk P.

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

Bibliografia

• [1] R. M. Blumenthal and R. K. Getoor, Markov' Processes and Potential Theory, Pure Appl. Math., Academic Press Inc., New York 1968.
• [2] K. Bogdan, The boundary Harnack principle for the fractional Laplacian, Studia Math. 123 (1997), pp. 43-80. -
• [3] N. Ikeda and S. Watanabe, On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2-1 (1962), pp. 79-95.
• [4] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Publishing Company, Amsterdam-Oxford-New York 1981.
• [5] P. W. Millar, Exit properties of stochastic processes with stationary independent increments, Trans. Amer. Math. Soc. 178 (1973), pp. 459-479.
• [6] P. W. Millar, First passage distributions of processes with independent increments, Ann. Probab. 3, No. 2 (1975), pp. 215-233.