The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564
  • Bass, Richard F.; Kassmann, Moritz. Harnack inequalities for non-local operators of variable order. Trans. Amer. Math. Soc. 357 (2005), no. 2, 837--850. MR2095633
  • Bass, Richard F.; Levin, David A. Harnack inequalities for jump processes. Potential Anal. 17 (2002), no. 4, 375--388. MR1918242
  • Bogdan, Krzysztof; Sztonyk, Paweł. Harnack's inequality for stable Lévy processes. Potential Anal. 22 (2005), no. 2, 133--150. MR2137058
  • Bogdan, Krzysztof; Stós, Andrzej; Sztonyk, Paweł. Potential theory for Lévy stable processes. Bull. Polish Acad. Sci. Math. 50 (2002), no. 3, 361--372. MR1948083
  • Chen, Zhen-Qing; Kumagai, Takashi. Heat kernel estimates for stable-like processes on $d$-sets. Stochastic Process. Appl. 108 (2003), no. 1, 27--62. MR2008600
  • Chen, Zhen-Qing; Kumagai, Takashi. Heat kernel estimates for jump processes of mixed types on metric measure spaces. Probab. Theory Related Fields 140 (2008), no. 1-2, 277--317. MR2357678
  • T. Grzywny and M. Ryznar, phPotential theory of one-dimensional geometric stable processes, preprint (2011).
  • Ikeda, Nobuyuki; Watanabe, Shinzo. On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes. J. Math. Kyoto Univ. 2 1962 79--95. MR0142153
  • Millar, P. W. First passage distributions of processes with independent increments. Ann. Probability 3 (1975), 215--233. MR0368177
  • Kim, Panki; Song, Renming. Potential theory of truncated stable processes. Math. Z. 256 (2007), no. 1, 139--173. MR2282263
  • P. Kim, R. Song and Z. Vondracek, phPotential theory for subordinate Brownian motions revisited, Interdisciplinary Mathematical Sciences - Vol. 13 STOCHASTIC ANALYSIS AND APPLICATIONS TO FINANCE, Essays in Honour of Jia-an Yan (2012).
  • P. Kim, R. Song and Z. Vondracek, phTwo-sided Green function estimates for killed subordinate Brownian motions, Proc. London Math. Soc. 104 (2012), 927--958.
  • Mimica, Ante. Harnack inequalities for some Lévy processes. Potential Anal. 32 (2010), no. 3, 275--303. MR2595368
  • Rao, Murali; Song, Renming; Vondraček, Zoran. Green function estimates and Harnack inequality for subordinate Brownian motions. Potential Anal. 25 (2006), no. 1, 1--27. MR2238934
  • Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520
  • Šikić, Hrvoje; Song, Renming; Vondraček, Zoran. Potential theory of geometric stable processes. Probab. Theory Related Fields 135 (2006), no. 4, 547--575. MR2240700
  • Schilling, René L.; Song, Renming; Vondraček, Zoran. Bernstein functions. Theory and applications. de Gruyter Studies in Mathematics, 37. Walter de Gruyter & Co., Berlin, 2010. xii+313 pp. ISBN: 978-3-11-021530-4 MR2598208
  • Song, Renming; Vondraček, Zoran. Harnack inequality for some classes of Markov processes. Math. Z. 246 (2004), no. 1-2, 177--202. MR2031452
  • Sztonyk, Paweł. On harmonic measure for Lévy processes. Probab. Math. Statist. 20 (2000), no. 2, Acta Univ. Wratislav. No. 2256, 383--390. MR1825650
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.