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

  1. Bertoin, Jean. On the local rate of growth of Lévy processes with no positive jumps. Stochastic Process. Appl. 55 (1995), no. 1, 91--100. MR1312150 (95k:60184)
  2. Bertoin, Jean. Lévy processes.Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564 (98e:60117)
  3. Bertoin, Jean. Subordinators: examples and applications. Lectures on probability theory and statistics (Saint-Flour, 1997), 1--91, Lecture Notes in Math., 1717, Springer, Berlin, 1999. MR1746300 (2002a:60001)
  4. Biggins, J. D. Random walk conditioned to stay positive. J. London Math. Soc. (2) 67 (2003), no. 1, 259--272. MR1942425 (2003m:60191)
  5. Bingham,N.; Goldie C.M. and Teugels J.L. Regular variation. Cambridge University Press, Cambridge, (1989). Math. Review 1015093
  6. Chaumont, L.; Doney, R. A. On Lévy processes conditioned to stay positive. Electron. J. Probab. 10 (2005), no. 28, 948--961 (electronic). MR2164035 (2006h:60079)
  7. Chaumont, Loic; Pardo, J. C. The lower envelope of positive self-similar Markov processes. Electron. J. Probab. 11 (2006), no. 49, 1321--1341 (electronic). MR2268546 (2008f:60042)
  8. Doney, Ronald A. Fluctuation theory for Lévy processes.Lectures from the 35th Summer School on Probability Theory held in Saint-Flour, July 6--23, 2005.Edited and with a foreword by Jean Picard.Lecture Notes in Mathematics, 1897. Springer, Berlin, 2007. x+147 pp. ISBN: 978-3-540-48510-0; 3-540-48510-4 MR2320889 (Review)
  9. Fristedt, Bert E. Sample function behavior of increasing processes with stationary, independent increments. Pacific J. Math. 21 1967 21--33. MR0210190 (35 #1084)
  10. Fristedt, Bert E.; Pruitt, William E. Lower functions for increasing random walks and subordinators. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 18 (1971), 167--182. MR0292163 (45 #1250)
  11. Gīhman, Ĭ. Ī.; Skorohod, A. V. The theory of stochastic processes. II.Translated from the Russian by Samuel Kotz.Die Grundlehren der Mathematischen Wissenschaften, Band 218.Springer-Verlag, New York-Heidelberg, 1975. vii+441 pp. MR0375463 (51 #11656)
  12. Hambly, B. M.; Kersting, G.; Kyprianou, A. E. Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative. Stochastic Process. Appl. 108 (2003), no. 2, 327--343. MR2019057 (2004m:60097)
  13. Monrad, Ditlev; Silverstein, Martin L. Stable processes: sample function growth at a local minimum. Z. Wahrsch. Verw. Gebiete 49 (1979), no. 2, 177--210. MR0543993 (80j:60102)
  14. Pardo, J. C. On the future infimum of positive self-similar Markov processes. Stochastics 78 (2006), no. 3, 123--155. MR2241913 (2008g:60113)
  15. J.C. Pardo. The upper envelope of positive self-similar Markov processes. To appear in J. Theoret. Probab., (2008).
Bookmark and Share


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