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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 463857, 12 pages
On the Laws of Total Local Times for -Paths and Bridges of Symmetric Lévy Processes
1Faculty of Science, University of the Ryukyus, 1 Senbaru, Okinawa, Nishihara 903-0213, Japan
2Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
Received 12 May 2012; Accepted 29 November 2012
Academic Editor: Dumitru Baleanu
Copyright © 2013 Masafumi Hayashi and Kouji Yano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. Applebaum, Lévy Processes and Stochastic Calculus, vol. 116 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 2nd edition, 2009.
- P. Imkeller and I. Pavlyukevich, “Lévy flights: transitions and meta-stability,” Journal of Physics A, vol. 39, no. 15, pp. L237–L246, 2006.
- D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, Germany, 3rd edition, 1999.
- M. Yor, Some Aspects of Brownian Motion. Part I, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, Switzerland, 1992.
- N. Eisenbaum and H. Kaspi, “A necessary and sufficient condition for the Markov property of the local time process,” The Annals of Probability, vol. 21, no. 3, pp. 1591–1598, 1993.
- N. Eisenbaum, H. Kaspi, M. B. Marcus, J. Rosen, and Z. Shi, “A Ray-Knight theorem for symmetric Markov processes,” The Annals of Probability, vol. 28, no. 4, pp. 1781–1796, 2000.
- K. Yano, “Excursions away from a regular point for one-dimensional symmetric Lévy processes without Gaussian part,” Potential Analysis, vol. 32, no. 4, pp. 305–341, 2010.
- K. Yano, Y. Yano, and M. Yor, “Penalising symmetric stable Lévy paths,” Journal of the Mathematical Society of Japan, vol. 61, no. 3, pp. 757–798, 2009.
- K. Yano, Y. Yano, and M. Yor, “On the laws of first hitting times of points for one-dimensional symmetric stable Lévy processes,” in Séminaire de Probabilités XLII, vol. 1979 of Lecture Notes in Mathematics, pp. 187–227, Springer, Berlin, Germany, 2009.
- K. Yano, “Two kinds of conditionings for stable Lévy processes,” in Probabilistic Approach to Geometry, vol. 57 of Advanced Studies in Pure Mathematic, pp. 493–503, Mathematical Society of Japan, Tokyo, Japan, 2010.
- R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, vol. 29 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1968.
- J. Pitman, “Cyclically stationary Brownian local time processes,” Probability Theory and Related Fields, vol. 106, no. 3, pp. 299–329, 1996.
- J. Pitman, “The distribution of local times of a Brownian bridge,” in Séminaire de Probabilités, XXXIII, vol. 1709 of Lecture Notes in Mathematics, pp. 388–394, Springer, Berlin, Germany, 1999.
- J. Pitman and M. Yor, “A decomposition of Bessel bridges,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 59, no. 4, pp. 425–457, 1982.
- P. Fitzsimmons, J. Pitman, and M. Yor, “Markovian bridges: construction, Palm interpretation, and splicing,” in Seminar on Stochastic Processes: Proceedings from 12th Seminar on Stochastic Processes, 1992, University of Washington, Seattle, Wash, USA, 1992, vol. 33 of Progress in Probability Series, pp. 101–134, Birkhäauser, Boston, Mass, USA, 1993.
- M. B. Marcus and J. Rosen, Markov Processes, Gaussian Processes, and Local Times, vol. 100 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 2006.
- J. Pitman and M. Yor, “Decomposition at the maximum for excursions and bridges of one-dimensional diffusions,” in Itô's Stochastic Calculus and Probability Theory, pp. 293–310, Springer, Tokyo, Japan, 1996.
- P. J. Fitzsimmons and K. Yano, “Time change approach to generalized excursion measures, and its application to limit theorems,” Journal of Theoretical Probability, vol. 21, no. 1, pp. 246–265, 2008.
- J. Bertoin, Lévy Processes, vol. 121 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK, 1996.
- S. Watanabe, K. Yano, and Y. Yano, “A density formula for the law of time spent on the positive side of one-dimensional diffusion processes,” Journal of Mathematics of Kyoto University, vol. 45, no. 4, pp. 781–806, 2005.