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


  • Albin, J. M. P. Extremes of totally skewed stable motion. Statist. Probab. Lett. 16 (1993), no. 3, 219--224. MR1208511
  • Albin, J. M. P.; Sundén, Mattias. On the asymptotic behaviour of Lévy processes. I. Subexponential and exponential processes. Stochastic Process. Appl. 119 (2009), no. 1, 281--304. MR2485028
  • Asmussen, Søren; Albrecher, Hansjörg. Ruin probabilities. Second edition. Advanced Series on Statistical Science & Applied Probability, 14. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010. xviii+602 pp. ISBN: 978-981-4282-52-9; 981-4282-52-9 MR2766220
  • Avram, F.; Kyprianou, A. E.; Pistorius, M. R. Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Ann. Appl. Probab. 14 (2004), no. 1, 215--238. MR2023021
  • Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran. The law of the supremum of a stable Lévy process with no negative jumps. Ann. Probab. 36 (2008), no. 5, 1777--1789. MR2440923
  • Bertoin, Jean. On the first exit time of a completely asymmetric stable process from a finite interval. Bull. London Math. Soc. 28 (1996), no. 5, 514--520. MR1396154
  • Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564
  • Borovkov, K.; Burq, Z. Kendall's identity for the first crossing time revisited. Electron. Comm. Probab. 6 (2001), 91--94. MR1871697
  • Furrer, Hansjörg; Michna, Zbigniew; Weron, Aleksander. Stable Lévy motion approximation in collective risk theory. Insurance Math. Econom. 20 (1997), no. 2, 97--114. MR1478842
  • Janicki, Aleksander; Weron, Aleksander. Simulation and chaotic behavior of $\alpha$-stable stochastic processes. Monographs and Textbooks in Pure and Applied Mathematics, 178. Marcel Dekker, Inc., New York, 1994. xii+355 pp. ISBN: 0-8247-8882-6 MR1306279
  • Kendall, David G. Some problems in theory of dams. J. Roy. Statist. Soc. Ser. B. 19 (1957), 207--212; discussion 212--233. MR0092290
  • Michna, Zbigniew. Formula for the supremum distribution of a spectrally positive $\alpha$-stable Lévy process. Statist. Probab. Lett. 81 (2011), no. 2, 231--235. MR2748187
  • Michna, Z.: Formula for the supremum distribution of a spectrally positive Lévy process, ARXIV1104.1976
  • Pistorius, M. R. On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum. J. Theoret. Probab. 17 (2004), no. 1, 183--220. MR2054585
  • Prabhu, N. U. On the ruin problem of collective risk theory. Ann. Math. Statist. 32 1961 757--764. MR0125645
  • Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
  • 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
  • Seal, Hilary L. The numerical calculation of $U(w,\,t)$, the probability of non-ruin in an interval $(O,\,t)$. Scand. Actuar. J. 1974, 121--139. MR0356295

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