One-dimensional symmetric stable Feynman-Kac semigroups

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

Abstrakty

EN

We investigate here one-dimensional Feynman-Kac semigroups based on symmetric α-stable processes. We begin with establishing the properties of Green operators of intervals and halflines on functions from the Kato class. Then we provide a sufficient condition for gaugeability of the halfline(−∞, b) and evaluate the critical value β.

Słowa kluczowe

EN

α-stable Léevy processes; Feynman-Kac semigroups on R1; potential theory; Kato class; Green operators; gauge function; gaugeability

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 381--404
• Opis fizyczny: Bibliogr.10 poz.

Twórcy

autor

Byczkowska H.

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

autor

Byczkowski T.

• 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 Their Potential Theory, Pure Appl. Math., Academic Press, New York 1968.
• [2] R. M, Blumenthal, R. K. Getoor and D. B. Ray, On the distribution of first hits for the symmetric stable processes, Trans, Amer, Math. Soc. 99 (1.961), pp. 540-554.
• [3] K. Bogdan and T. Byczkowski, Potential theory for the astable Schrödinger operator on bounded Lipschitz domains, Studia Math. 133 (1999), pp. 53-92.
• [4] K. Bogdan and T. Byczkowski, Potential theory of Schrödinger operator based on fractional Laplacian, Probab. Math. Statist. 20 (2000), pp. 293-335.
• [5] Z.-Q. Chen and R. Song, Intrinsic ultracontractivity and conditional gauge for symmetric stable processes, 3. Funct. Anal. 150 (1997), pp. 204-239.
• [6] Z.-Q, Chen and R. Song, Intrinsic ultracontractivity, conditional lifetimes and conditional gauge for symmetric stable processes on rough domains, Illinois 1 Math. 44 (2000), pp. 138-160.
• [7] K. L. Chung and Z. Zhao, From Brownian Motion to Schrödinger's Equation, Springer, New York 1995.
• [8] D, B. Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc. 89 (1958), pp. 16-24.
• [9] K. Samotij, Non-Brownian Schrödinger operators, preprint, 1997, pp. 1-35.
• [10] Z. Zhao, A probabilistic principle and generalized Schrödinger perturbation, J. Funct, Anal. 101 (1991), pp. 162-176.