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
  • Blumenthal, R. M.; Getoor, R. K. Some theorems on stable processes. Trans. Amer. Math. Soc. 95 1960 263--273. MR0119247
  • Bogdan, Krzysztof; Burdzy, Krzysztof; Chen, Zhen-Qing. Censored stable processes. Probab. Theory Related Fields 127 (2003), no. 1, 89--152. MR2006232
  • Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michał. Heat kernel estimates for the fractional Laplacian with Dirichlet conditions. Ann. Probab. 38 (2010), no. 5, 1901--1923. MR2722789
  • Chen, Zhen-Qing; Kim, Panki; Song, Renming. Heat kernel estimates for the Dirichlet fractional Laplacian. J. Eur. Math. Soc. (JEMS) 12 (2010), no. 5, 1307--1329. MR2677618
  • Chen, Zhen-Qing; Kim, Panki; Song, Renming. Heat kernel estimates for $\Delta+\Delta^ {\alpha/2}$ in $C^ {1,1}$ open sets. J. Lond. Math. Soc. (2) 84 (2011), no. 1, 58--80. MR2819690
  • Z.-Q. Chen, P. Kim, and R. Song: Global heat kernel estimates for relativistic stable processes in half-space-like open sets. Potential Anal., 36 (2012) 235--261.
  • Chen, Zhen-Qing; Kim, Panki; Song, Renming; Vondraček, Zoran. Boundary Harnack principle for $\Delta+\Delta^ {\alpha/2}$. Trans. Amer. Math. Soc. 364 (2012), no. 8, 4169--4205. MR2912450
  • 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
  • Chen, Zhen-Qing; Kumagai, Takashi. A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. Rev. Mat. Iberoam. 26 (2010), no. 2, 551--589. MR2677007
  • Chen, Zhen-Qing; Tokle, Joshua. Global heat kernel estimates for fractional Laplacians in unbounded open sets. Probab. Theory Related Fields 149 (2011), no. 3-4, 373--395. MR2776619
  • Q.-Y. Guan: Boundary Harnack inequality for regional fractional Laplacian. arXiv:0705.1614v3 [math.PR]
  • Kim, Panki; Song, Renming. Potential theory of truncated stable processes. Math. Z. 256 (2007), no. 1, 139--173. MR2282263
  • Kim, Panki; Song, Renming; Vondraček, Zoran. Boundary Harnack principle for subordinate Brownian motions. Stochastic Process. Appl. 119 (2009), no. 5, 1601--1631. MR2513121
  • Kim, Panki; Song, Renming; Vondraček, Zoran. On the potential theory of one-dimensional subordinate Brownian motions with continuous components. Potential Anal. 33 (2010), no. 2, 153--173. MR2658980
  • P. Kim, R. Song and Z. Vondracek: Minimal thinness for subordinate Brownian motion in half space. To appear in Ann. Inst. Fourier (Grenoble).
  • 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
  • Silverstein, Martin L. Classification of coharmonic and coinvariant functions for a Lévy process. Ann. Probab. 8 (1980), no. 3, 539--575. MR0573292
  • Skorohod, A. V. Random processes with independent increments. Translated from the second Russian edition by P. V. Malyshev. Mathematics and its Applications (Soviet Series), 47. Kluwer Academic Publishers Group, Dordrecht, 1991. xii+279 pp. ISBN: 0-7923-0340-7 MR1155400
  • Song, Renming. Estimates on the Dirichlet heat kernel of domains above the graphs of bounded $C^ {1,1}$ functions. Glas. Mat. Ser. III 39(59) (2004), no. 2, 273--286. MR2109269
  • Song, Renming; Vondraček, Zoran. Potential theory of special subordinators and subordinate killed stable processes. J. Theoret. Probab. 19 (2006), no. 4, 817--847. MR2279605
  • Song, Renming; Vondraček, Zoran. Parabolic Harnack inequality for the mixture of Brownian motion and stable process. Tohoku Math. J. (2) 59 (2007), no. 1, 1--19. MR2321989
Bookmark and Share


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