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Abstrakty
In this paper, we calculate the principal eigenvalues for time changed processes of Brownian motions and symmetric α-stable processes in one dimension.
Czasopismo
Rocznik
Tom
Strony
355--366
Opis fizyczny
Bibliogr. 13 poz., wykr.
Twórcy
autor
- Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan
Bibliografia
- [1] S. Albeverio, P. Blanchard and Z. M. Ma, Feynman-Kac semigroups in terms of signed smooth measures, in: Random Partial Differential Equations, U. Hornung et al. (Eds.), Birkhäuser, Basel 1991, pp. 1-31.
- [2] R. Bañuelos and T. Kulczycki, The Cauchy process and Steklov problem, J. Funct. Anal. 211 (2004), pp. 355-423.
- [3] R. Bañuelos, R Latala and P. J. Méndez-Hernández, A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes, Proc. Amer. Math. Soc. 129 (2001), pp. 2997-3008.
- [4] A. N. Borodin and P. Salminen, Handbook of Brownian Motion - Facts and Formulae, Probability and Its Application, Birkhäuser, Basel 1996.
- [5] Z. Q. Chen, Gaugeability and conditional gaugeability, Trans. Amer. Math. Soc. 354 (2002), pp. 4639-4679.
- [6] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin 1994.
- [7] R. K. Getoor, Continuous additive functionals of a Markov process with applications to processes with independent increments, J. Math. Anal. Appl. 13 (1966), pp. 132-153.
- [8] R. Z. Khas'minskii, On positive solutions of the equation Uu+ Vu = 0, Theory Probab. Appl. 4 (1959), pp. 309-318.
- [9] S. C. Port, Hitting times and potentials for recurrent stable processes, J. Anal. Math. 20 (1967), pp. 371-395.
- [10] Y. Shiozawa and M. Takeda, Variational formula for Dirichlet forms and estimates of principal eigenvalues for symmetric α-stable processes, Potential Anal. [to appear).
- [11] M. Takeda, Conditional gaugeability and subcriticality of generalized Schrödinger operators, J. Funct. Anal. 191 (2002), pp. 343-376.
- [12] M. Takeda, Gaugeability for Feynman-Kuc functionals with applications to symmetric α-stable processes, preprint (2004).
- [13] M. Takeda and T. Uemura, Subcriticality and gaugeability for symmetric α-stable processes, Forum Math 16 (2004), pp. 505-517.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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