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. Allouba, Hassan; Zheng, Weian. Brownian-time processes: the PDE connection and the half-derivative generator. Ann. Probab. 29 (2001), no. 4, 1780--1795. MR1880242 (2002j:60118)
  2. Anderson, Theodore W. The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6, (1955). 170--176. MR0069229 (16,1005a)
  3. Aurzada, Frank. Small deviations for stable processes via compactness properties of the parameter set. Statist. Probab. Lett. 78 (2008), no. 6, 577--581. MR2409520 (2009h:60083)
  4. 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)
  5. Bingham, Nick H.; Goldie, Charles M.; Teugels, Jozef L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1989. xx+494 pp. ISBN: 0-521-37943-1 MR1015093 (90i:26003)
  6. Blackburn, Robert. Large deviations of local times of Lévy processes. J. Theoret. Probab. 13 (2000), no. 3, 825--842. MR1785531 (2001h:60084)
  7. Borovkov, A. A.; Mogulʹskiĭ, A. A. On probabilities of small deviations for stochastic processes [translation of Trudy Inst. Mat. (Novosibirsk) 13 (1989), Asimptot. Analiz Raspred. Sluch. Protsess., 147--168; MR1037254 (91e:60089)]. Siberian Advances in Mathematics. Siberian Adv. Math. 1 (1991), no. 1, 39--63. MR1100316
  8. Burdzy, Krzysztof. Some path properties of iterated Brownian motion. Seminar on Stochastic Processes, 1992 (Seattle, WA, 1992), 67--87, Progr. Probab., 33, Birkhäuser Boston, Boston, MA, 1993. MR1278077 (95c:60075)
  9. Burdzy, Krzysztof. Variation of iterated Brownian motion. Measure-valued processes, stochastic partial differential equations, and interacting systems (Montreal, PQ, 1992), 35--53, CRM Proc. Lecture Notes, 5, Amer. Math. Soc., Providence, RI, 1994. MR1278281 (95h:60123)
  10. Embrechts, Paul; Maejima, Makoto. Selfsimilar processes. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2002. xii+111 pp. ISBN: 0-691-09627-9 MR1920153 (2004c:60003)
  11. Hu, Yueyun; Pierre-Loti-Viaud, Daniel; Shi, Zhan. Laws of the iterated logarithm for iterated Wiener processes. J. Theoret. Probab. 8 (1995), no. 2, 303--319. MR1325853 (96b:60073)
  12. Khoshnevisan, Davar; Lewis, Thomas M. Chung's law of the iterated logarithm for iterated Brownian motion. Ann. Inst. H. Poincaré Probab. Statist. 32 (1996), no. 3, 349--359. MR1387394 (97k:60218)
  13. Khoshnevisan, Davar; Xiao, Yimin. Lévy processes: capacity and Hausdorff dimension. Ann. Probab. 33 (2005), no. 3, 841--878. MR2135306 (2006d:60078)
  14. Lacey, Michael. Large deviations for the maximum local time of stable Lévy processes. Ann. Probab. 18 (1990), no. 4, 1669--1675. MR1071817 (91h:60085)
  15. Li, Wenbo V. A Gaussian correlation inequality and its applications to small ball probabilities. Electron. Comm. Probab. 4 (1999), 111--118 (electronic). MR1741737 (2001j:60074)
  16. Li, Wenbo V.; Shao, Qi-Man. Gaussian processes: inequalities, small ball probabilities and applications. Stochastic processes: theory and methods, 533--597, Handbook of Statist., 19, North-Holland, Amsterdam, 2001. MR1861734
  17. Lifshits, Mikhail; Simon, Thomas. Small deviations for fractional stable processes. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 4, 725--752. MR2144231 (2006d:60081)
  18. Lifshits, Mikhail. Asymptotic behavior of small ball probabilities. Probab. Theory and Math. Statist. Proc. VII International Vilnius Conference, 1999, pp. 453--468. Math. Review number not available.
  19. Lifshits, Mikhail. Bibliography compilation on small deviation probabilities, available from http://www.proba.jussieu.fr/pageperso/smalldev/biblio.html, 2009. Math. Review number not available.
  20. Liggett, Thomas M. Interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231 (86e:60089)
  21. Linde, Werner; Shi, Zhan. Evaluating the small deviation probabilities for subordinated Lévy processes. Stochastic Process. Appl. 113 (2004), no. 2, 273--287. MR2087961 (2005h:60139)
  22. Linde, Werner; Zipfel, Pia. Small deviation of subordinated processes over compact sets. Probab. Math. Statist. 28 (2008), no. 2, 281--304. Math. Review number not yet available.
  23. Mogulʹskiĭ, A. A. Small deviations in the space of trajectories. (Russian) Teor. Verojatnost. i Primenen. 19 (1974), 755--765. MR0370701 (51 #6927)
  24. Nane, Erkan. Laws of the iterated logarithm for $alpha$-time Brownian motion. Electron. J. Probab. 11 (2006), no. 18, 434--459 (electronic). MR2223043 (2007c:60087)
  25. Nourdin, Ivan; Peccati, Giovanni. Weighted power variations of iterated Brownian motion. Electron. J. Probab. 13 (2008), no. 43, 1229--1256. MR2430706 (2009h:60052)
  26. Pruitt, William E. The Hausdorff dimension of the range of a process with stationary independent increments. J. Math. Mech. 19 1969/1970 371--378. MR0247673 (40 #936)
  27. Samorodnitsky, Gennady. Lower tails of self-similar stable processes. Bernoulli 4 (1998), no. 1, 127--142. MR1611887 (99e:60105)
  28. 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 (95f:60024)
  29. Shi, Zhan. Lower limits of iterated Wiener processes. Statist. Probab. Lett. 23 (1995), no. 3, 259--270. MR1340161 (96m:60077)
  30. Taylor, S. James. Sample path properties of a transient stable process. J. Math. Mech. 16 1967 1229--1246. MR0208684 (34 #8493)
  31. Vervaat, Wim. Sample path properties of self-similar processes with stationary increments. Ann. Probab. 13 (1985), no. 1, 1--27. MR0770625 (86c:60063)


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