A family of symmetric stable-like processes and its global path properties

• Autorzy: Isozaki Y. , Uemura T.
• Języki publikacji: EN

Abstrakty

EN

We extend the idea of the symmetric stable-like processes so that it includes the Brownian motion as well as the symmetric α-stable processes. We exhibit some sufficient conditions for their recurrence and conservativeness relying on the no-tion of Dirichlet forms. A criterion for conservativeness (Lemma 3.2) is also shown in terms of general Dirichlet forms and the associated generators.

Słowa kluczowe

EN

stable-like processes; recurrence; transience

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 1
• Strony: 145--164
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Isozaki Y.

• Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan

autor

Uemura T.

• Department of Management Science, Kobe University of Commerce, Nishi-ku, Kobe, 651-2197, Japan

Bibliografia

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• [5] M. Fukushima, Y. Oshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin 1994.
• [6] N. Jacob and R. L. Schilling, Lévy-type processes and pseudodifferential opetrators, in: Lévy Processes: Theory and Applications, O. E. Barndorff-Nielsen et al. (Eds.), Birkhäuser, Princeton 2001, pp. 139-167.
• [7] A. Negoro, Stable-like processes: construction of the transition density and the behavior of sample paths near t = 0, Osaka J. Math. 31 (1994), pp. 189-214.
• [8] Y. Ogura, M. Tomisaki and M. Tsuchiya, Convergence of local type Dirichlet forms to a non-local type one, Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), pp. 507-556.
• [9] R. L. Schilling, Conservativeness of semigroups generated by pseudo-differential operators, Potential Anal. 9 (1998), pp. 91-104.
• [10] M. Tsuchiya, Lévy measure with generalized polar decomposition and the associated SDE with jumps, Stochastics Stochastics Rep. 38 (1992), pp. 95-117.
• [11] T. Uemura, On some path properties of symmetric stable-like processes for one dimension, Potential Anal. 16 (2002), pp. 79-91.
• [12] T. Uemura, On symmetric stable-like processes: Some path properties and generators, J. Theoret. Probab. (to appear).

Uwagi

Dedicated to Professor Yoichi Oshima on the occasion of His sixtieth birthday.