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. Aurzada, F.; Dereich, S.. Universality of the asymptotics of the one-sided exit problem for integrated processes. To appear in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011+, arXiv:1008.0485.
  2. Bertoin, J.. The inviscid Burgers equation with Brownian initial velocity. Comm. Math. Phys. 193 (1998), no. 2, 397--406. MR1618139 (2000a:35208)
  3. Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1989. xx+494 pp. MR1015093 (90i:26003)
  4. Li, W. V.; Shao, Q.. Lower tail probabilities for Gaussian processes. Ann. Probab. 32 (2004), no. 1A, 216--242. MR2040781 (2005f:60094)
  5. Molchan, G. M. Maximum of a fractional Brownian motion: probabilities of small values. Comm. Math. Phys. 205 (1999), no. 1, 97--111. MR1706900 (2000i:60094)
  6. Molchan, G. M. On the maximum of fractional Brownian motion. (Russian) Teor. Veroyatnost. i Primenen. 44 (1999), no. 1, 111--115; translation in Theory Probab. Appl. 44 (2000), no. 1, 97--102 MR1751192 (2001a:60027)
  7. Molchan, G. Unilateral small deviations of processes related to the fractional Brownian motion. Stochastic Process. Appl. 118 (2008), no. 11, 2085--2097. MR2462290 (2010b:60114)
  8. She, Z.; Aurell, E.; Frisch, U.. The inviscid Burgers equation with initial data of Brownian type. Comm. Math. Phys. 148 (1992), no. 3, 623--641. MR1181072 (93h:35182)
  9. Scheutzow, M.. Chaining techniques and their application to stochastic flows. Trends in stochastic analysis, 35--63, London Math. Soc. Lecture Note Ser., 353, Cambridge Univ. Press, Cambridge, 2009. MR2562150 (2011c:60210)
  10. Sinaĭ, Ya. G. On the distribution of the maximum of fractional Brownian motion. (Russian) Uspekhi Mat. Nauk 52 (1997), no. 2(314), 119--138; translation in Russian Math. Surveys 52 (1997), no. 2, 359--378 MR1480141 (99j:60050)
  11. Slepian, D.. The one-sided barrier problem for Gaussian noise. Bell System Tech. J. 41 1962 463--501. MR0133183 (24 #A3017)
  12. Uchiyama, K.. Brownian first exit from and sojourn over one-sided moving boundary and application. Z. Wahrsch. Verw. Gebiete 54 (1980), no. 1, 75--116. MR0595482 (82c:60143)


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